2.4.21 second order kovacic

Table 2.491: second order kovacic

#

ODE

CAS classification

Solved?

11

\[ {}x^{\prime \prime } = 50 \]
i.c.

[[_2nd_order, _quadrature]]

12

\[ {}x^{\prime \prime } = -20 \]
i.c.

[[_2nd_order, _quadrature]]

13

\[ {}x^{\prime \prime } = 3 t \]
i.c.

[[_2nd_order, _quadrature]]

14

\[ {}x^{\prime \prime } = 2 t +1 \]
i.c.

[[_2nd_order, _quadrature]]

15

\[ {}x^{\prime \prime } = 4 \left (3+t \right )^{2} \]
i.c.

[[_2nd_order, _quadrature]]

16

\[ {}x^{\prime \prime } = \frac {1}{\sqrt {t +4}} \]
i.c.

[[_2nd_order, _quadrature]]

17

\[ {}x^{\prime \prime } = \frac {1}{\left (t +1\right )^{3}} \]
i.c.

[[_2nd_order, _quadrature]]

18

\[ {}x^{\prime \prime } = 50 \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _quadrature]]

147

\[ {}x y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_y]]

149

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

150

\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \]

[[_2nd_order, _missing_y]]

152

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime } = 2 \]

[[_2nd_order, _missing_y]]

215

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

216

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

217

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

218

\[ {}y^{\prime \prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

219

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

220

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

221

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

222

\[ {}y^{\prime \prime }-3 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

223

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

224

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

225

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

226

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

227

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

228

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

229

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

230

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

234

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

235

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

[[_2nd_order, _missing_x]]

236

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

237

\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

238

\[ {}2 y^{\prime \prime }-y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

239

\[ {}4 y^{\prime \prime }+8 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

240

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

241

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

242

\[ {}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0 \]

[[_2nd_order, _missing_x]]

243

\[ {}35 y^{\prime \prime }-y^{\prime }-12 y = 0 \]

[[_2nd_order, _missing_x]]

244

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

245

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

[[_Emden, _Fowler]]

246

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

247

\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

248

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

257

\[ {}y^{\prime \prime }+y = 3 x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

258

\[ {}y^{\prime \prime }-4 y = 12 \]
i.c.

[[_2nd_order, _missing_x]]

259

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \]
i.c.

[[_2nd_order, _missing_x]]

260

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 2 x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

261

\[ {}y^{\prime \prime }+2 y = 6 x +4 \]

[[_2nd_order, _with_linear_symmetries]]

262

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

263

\[ {}y^{\prime \prime }-2 y^{\prime }-5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

271

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

272

\[ {}2 y^{\prime \prime }-3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

273

\[ {}y^{\prime \prime }+y^{\prime }-10 y = 0 \]

[[_2nd_order, _missing_x]]

274

\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

275

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

276

\[ {}y^{\prime \prime }+5 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

277

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

278

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

279

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

291

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

292

\[ {}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

293

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

309

\[ {}y^{\prime \prime }+2 i y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

310

\[ {}y^{\prime \prime }-i y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

311

\[ {}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y \]

[[_2nd_order, _missing_x]]

315

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

316

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \]

[[_Emden, _Fowler]]

322

\[ {}y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

323

\[ {}y^{\prime \prime }-y^{\prime }+2 y = 3 x +4 \]

[[_2nd_order, _with_linear_symmetries]]

324

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

325

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

326

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

327

\[ {}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

328

\[ {}y^{\prime \prime }-4 y = \sinh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

329

\[ {}y^{\prime \prime }-4 y = \cosh \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

330

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

331

\[ {}2 y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

334

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

337

\[ {}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \]

[[_2nd_order, _linear, _nonhomogeneous]]

338

\[ {}y^{\prime \prime }+y = x \cos \left (x \right )+\sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

342

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

344

\[ {}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

346

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

347

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

351

\[ {}y^{\prime \prime }+4 y = 2 x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

352

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

353

\[ {}y^{\prime \prime }+9 y = \sin \left (2 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

354

\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

355

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = x +1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

358

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (3 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

363

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

364

\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

365

\[ {}y^{\prime \prime }+y = x \cos \left (x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

366

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

367

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

368

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

369

\[ {}y^{\prime \prime }-4 y = \sinh \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

370

\[ {}y^{\prime \prime }+4 y = \cos \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

371

\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

372

\[ {}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

373

\[ {}y^{\prime \prime }+y = \csc \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

374

\[ {}y^{\prime \prime }+4 y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

375

\[ {}y^{\prime \prime }-4 y = x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

376

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

377

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

378

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4} \]

[[_2nd_order, _with_linear_symmetries]]

379

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}} \]

[[_2nd_order, _with_linear_symmetries]]

380

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

381

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1 \]

[[_2nd_order, _with_linear_symmetries]]

382

\[ {}y^{\prime \prime }+y = 2 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

383

\[ {}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

384

\[ {}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

385

\[ {}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

386

\[ {}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

387

\[ {}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

388

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

389

\[ {}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

390

\[ {}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

391

\[ {}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

392

\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

393

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

394

\[ {}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

395

\[ {}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

396

\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 2 \cos \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

397

\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

398

\[ {}x^{\prime \prime }+6 x^{\prime }+45 x = 50 \cos \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

399

\[ {}x^{\prime \prime }+10 x^{\prime }+650 x = 100 \cos \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

516

\[ {}x y^{\prime \prime }-y^{\prime }+36 x^{3} y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

522

\[ {}16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

526

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

807

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

808

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

809

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

810

\[ {}y^{\prime \prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

811

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

812

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

813

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

814

\[ {}y^{\prime \prime }-3 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

815

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

816

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

817

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

818

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

819

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

820

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

821

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

822

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

823

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

824

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

[[_2nd_order, _missing_x]]

825

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

826

\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

827

\[ {}2 y^{\prime \prime }-y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

828

\[ {}4 y^{\prime \prime }+8 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

829

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

830

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

831

\[ {}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0 \]

[[_2nd_order, _missing_x]]

832

\[ {}35 y^{\prime \prime }-y^{\prime }-12 y = 0 \]

[[_2nd_order, _missing_x]]

833

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

834

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

[[_Emden, _Fowler]]

835

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

836

\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

837

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

838

\[ {}y^{\prime \prime }+y = 3 x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

839

\[ {}y^{\prime \prime }-4 y = 12 \]
i.c.

[[_2nd_order, _missing_x]]

840

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \]
i.c.

[[_2nd_order, _missing_x]]

841

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 2 x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

842

\[ {}y^{\prime \prime }+2 y = 4 \]

[[_2nd_order, _missing_x]]

843

\[ {}y^{\prime \prime }+2 y = 6 x \]

[[_2nd_order, _with_linear_symmetries]]

844

\[ {}y^{\prime \prime }+2 y = 6 x +4 \]

[[_2nd_order, _with_linear_symmetries]]

845

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

846

\[ {}2 y^{\prime \prime }-3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

847

\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 0 \]

[[_2nd_order, _missing_x]]

848

\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

849

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

850

\[ {}y^{\prime \prime }+5 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

851

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

852

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

853

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

854

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

855

\[ {}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

856

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

857

\[ {}y^{\prime \prime }-2 i y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

858

\[ {}y^{\prime \prime }-i y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

859

\[ {}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y \]

[[_2nd_order, _missing_x]]

860

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

861

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \]

[[_Emden, _Fowler]]

862

\[ {}\frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

863

\[ {}3 x^{\prime \prime }+30 x^{\prime }+63 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

864

\[ {}x^{\prime \prime }+8 x^{\prime }+16 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

865

\[ {}2 x^{\prime \prime }+12 x^{\prime }+50 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

866

\[ {}4 x^{\prime \prime }+20 x^{\prime }+169 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

867

\[ {}2 x^{\prime \prime }+16 x^{\prime }+40 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

868

\[ {}x^{\prime \prime }+10 x^{\prime }+125 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

869

\[ {}y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

870

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 3 x +4 \]

[[_2nd_order, _with_linear_symmetries]]

871

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

872

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

873

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

874

\[ {}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

875

\[ {}y^{\prime \prime }-4 y = \sinh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

876

\[ {}y^{\prime \prime }-4 y = \cosh \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

877

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

878

\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

879

\[ {}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \]

[[_2nd_order, _linear, _nonhomogeneous]]

880

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

881

\[ {}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

882

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

883

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

884

\[ {}y^{\prime \prime }+4 y = 2 x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

885

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

886

\[ {}y^{\prime \prime }+9 y = \sin \left (2 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

887

\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

888

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = x +1 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

889

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

890

\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

891

\[ {}y^{\prime \prime }+y = x \cos \left (x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

892

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

893

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

894

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

895

\[ {}y^{\prime \prime }-4 y = \sinh \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

896

\[ {}y^{\prime \prime }+4 y = \cos \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

897

\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

898

\[ {}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

899

\[ {}y^{\prime \prime }+y = \csc \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

900

\[ {}y^{\prime \prime }+4 y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

901

\[ {}y^{\prime \prime }-4 y = x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

902

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

903

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

904

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4} \]

[[_2nd_order, _with_linear_symmetries]]

905

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}} \]

[[_2nd_order, _with_linear_symmetries]]

906

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

907

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1 \]

[[_2nd_order, _with_linear_symmetries]]

908

\[ {}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

909

\[ {}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

910

\[ {}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

911

\[ {}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

912

\[ {}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

913

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

914

\[ {}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

915

\[ {}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

916

\[ {}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

917

\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

918

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

919

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

920

\[ {}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

921

\[ {}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1249

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

1250

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

1251

\[ {}6 y^{\prime \prime }-y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

1252

\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

1253

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

1254

\[ {}4 y^{\prime \prime }-9 y = 0 \]

[[_2nd_order, _missing_x]]

1255

\[ {}y^{\prime \prime }-9 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

1256

\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

1257

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1258

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1259

\[ {}6 y^{\prime \prime }-5 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1260

\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1261

\[ {}y^{\prime \prime }+5 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1262

\[ {}2 y^{\prime \prime }+y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1263

\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1264

\[ {}4 y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1265

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1266

\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1267

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1268

\[ {}4 y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1269

\[ {}y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y = 0 \]

[[_2nd_order, _missing_x]]

1270

\[ {}y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y = 0 \]

[[_2nd_order, _missing_x]]

1271

\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1272

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1273

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

1274

\[ {}y^{\prime \prime }-2 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

1275

\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 0 \]

[[_2nd_order, _missing_x]]

1276

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

1277

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

1278

\[ {}4 y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

1279

\[ {}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0 \]

[[_2nd_order, _missing_x]]

1280

\[ {}9 y^{\prime \prime }+9 y^{\prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

1281

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0 \]

[[_2nd_order, _missing_x]]

1282

\[ {}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0 \]

[[_2nd_order, _missing_x]]

1283

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1284

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1285

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1286

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1287

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1288

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1289

\[ {}u^{\prime \prime }-u^{\prime }+2 u = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1290

\[ {}5 u^{\prime \prime }+2 u^{\prime }+7 u = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1291

\[ {}y^{\prime \prime }+2 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1292

\[ {}y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1293

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1294

\[ {}t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1295

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4} = 0 \]

[[_Emden, _Fowler]]

1296

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1297

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1298

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

1299

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y = 0 \]

[[_Emden, _Fowler]]

1300

\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y = 0 \]

[[_Emden, _Fowler]]

1302

\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1303

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

1304

\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

1305

\[ {}4 y^{\prime \prime }-4 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

1306

\[ {}4 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

1307

\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

1308

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

1309

\[ {}4 y^{\prime \prime }+17 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

1310

\[ {}16 y^{\prime \prime }+24 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

1311

\[ {}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

1312

\[ {}2 y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

1313

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1314

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1315

\[ {}9 y^{\prime \prime }+6 y^{\prime }+82 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1316

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1317

\[ {}4 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1318

\[ {}y^{\prime \prime }-y^{\prime }+\frac {y}{4} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1327

\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1328

\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4} = 0 \]

[[_Emden, _Fowler]]

1329

\[ {}2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

1330

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1331

\[ {}4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

1332

\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y = 0 \]

[[_Emden, _Fowler]]

1333

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

1334

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

1335

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

1336

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \]

[[_2nd_order, _with_linear_symmetries]]

1337

\[ {}y^{\prime \prime }+y = \tan \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1338

\[ {}y^{\prime \prime }+9 y = 9 \sec \left (3 t \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1339

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 t}}{t^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1340

\[ {}y^{\prime \prime }+4 y = 3 \csc \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1341

\[ {}y^{\prime \prime }+y = 2 \sec \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1342

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1343

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1344

\[ {}y^{\prime \prime }+4 y = g \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1345

\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1346

\[ {}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3} \]

[[_2nd_order, _with_linear_symmetries]]

1347

\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t} \]

[[_2nd_order, _with_linear_symmetries]]

1348

\[ {}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

1349

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1350

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1351

\[ {}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

1352

\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1353

\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t} \]

[[_2nd_order, _with_linear_symmetries]]

1354

\[ {}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right ) {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

1355

\[ {}u^{\prime \prime }+2 u = 0 \]

[[_2nd_order, _missing_x]]

1356

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1357

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1358

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1359

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1517

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1737

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1738

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1739

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1740

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1741

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1742

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

1743

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

1744

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

1745

\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

1746

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1747

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

1748

\[ {}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0 \]

[[_Emden, _Fowler]]

1749

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1750

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1751

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1754

\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1756

\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1805

\[ {}y^{\prime \prime }+9 y = \tan \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1806

\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \sec \left (2 x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1807

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {4}{1+{\mathrm e}^{-x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1808

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 3 \,{\mathrm e}^{x} \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1809

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 14 x^{{3}/{2}} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1810

\[ {}y^{\prime \prime }-y = \frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1811

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 2 x^{2}+2 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1812

\[ {}x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (-2+x \right ) y = {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1813

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1814

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 4 \,{\mathrm e}^{-x \left (2+x \right )} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1815

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{{5}/{2}} \]

[[_2nd_order, _with_linear_symmetries]]

1816

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{4} \sin \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

1817

\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1819

\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 6 x^{3} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1820

\[ {}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = x^{a +1} \]

[[_2nd_order, _with_linear_symmetries]]

1821

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = x^{3} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1822

\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1824

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 8 x^{{5}/{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1825

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = x^{{7}/{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1826

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 3 x^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1827

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = x^{3} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1828

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = x^{{3}/{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1829

\[ {}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y = x^{4} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1830

\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 2 x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1831

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = x^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1832

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 2 \left (-1+x \right )^{2} {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

1833

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = x^{{5}/{2}} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1834

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1835

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+2 y = \left (-1+x \right )^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1836

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (x +1\right ) y = \left (-1+x \right )^{3} {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1837

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1838

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = -2 x^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1839

\[ {}\left (x +1\right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y = \left (2 x +3\right )^{2} \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2362

\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

2363

\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

2364

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

2365

\[ {}6 y^{\prime \prime }-7 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2366

\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2367

\[ {}3 y^{\prime \prime }+6 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

2368

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2369

\[ {}2 y^{\prime \prime }+y^{\prime }-10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2370

\[ {}5 y^{\prime \prime }+5 y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2371

\[ {}y^{\prime \prime }-6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2372

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2373

\[ {}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0 \]

[[_Emden, _Fowler]]

2374

\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0 \]

[[_Emden, _Fowler]]

2375

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0 \]
i.c.

[[_Emden, _Fowler]]

2376

\[ {}y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2377

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2378

\[ {}2 y^{\prime \prime }+3 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

2379

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

2380

\[ {}4 y^{\prime \prime }-y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2381

\[ {}y^{\prime \prime }+y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2382

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2383

\[ {}2 y^{\prime \prime }-y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2384

\[ {}3 y^{\prime \prime }-2 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2385

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2386

\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

2387

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

2388

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

2389

\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2390

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2391

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2392

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2393

\[ {}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2394

\[ {}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2395

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \]

[_Gegenbauer]

2396

\[ {}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2397

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \]

[_Gegenbauer]

2398

\[ {}\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2399

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2400

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2401

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

2402

\[ {}y^{\prime \prime }+y = \sec \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2403

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2404

\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2405

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

2406

\[ {}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2407

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = t^{{5}/{2}} {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2408

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2409

\[ {}y^{\prime \prime }-y = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2411

\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1 \]

[[_2nd_order, _with_linear_symmetries]]

2412

\[ {}m y^{\prime \prime }+c y^{\prime }+k y = F_{0} \cos \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2431

\[ {}t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

2432

\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0 \]

[[_Emden, _Fowler]]

2433

\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2434

\[ {}\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2435

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2436

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

2437

\[ {}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2438

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2439

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler]]

2440

\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2543

\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

2544

\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

2545

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

2546

\[ {}6 y^{\prime \prime }-7 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2547

\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2548

\[ {}3 y^{\prime \prime }+6 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

2549

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2550

\[ {}2 y^{\prime \prime }+y^{\prime }-10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2551

\[ {}5 y^{\prime \prime }+5 y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2552

\[ {}y^{\prime \prime }-6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2553

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2554

\[ {}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0 \]

[[_Emden, _Fowler]]

2555

\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y = 0 \]
i.c.

[[_Emden, _Fowler]]

2556

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2557

\[ {}2 y^{\prime \prime }+3 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

2558

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

2559

\[ {}4 y^{\prime \prime }-y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2560

\[ {}y^{\prime \prime }+y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2561

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2562

\[ {}2 y^{\prime \prime }-y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2563

\[ {}3 y^{\prime \prime }-2 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2564

\[ {}y^{\prime \prime }+w^{2} y = 0 \]

[[_2nd_order, _missing_x]]

2565

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2566

\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

2567

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

2568

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

2569

\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2570

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2571

\[ {}6 y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2572

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2581

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2582

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

2583

\[ {}y^{\prime \prime }+y = \sec \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2584

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2585

\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2586

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

2587

\[ {}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2588

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = t^{{5}/{2}} {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2589

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2590

\[ {}y^{\prime \prime }-y = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2591

\[ {}t^{2} y^{\prime \prime }-2 y = t^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2593

\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1 \]

[[_2nd_order, _with_linear_symmetries]]

2594

\[ {}y^{\prime \prime }+3 y = t^{3}-1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

2595

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = t \,{\mathrm e}^{\alpha t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2596

\[ {}y^{\prime \prime }-y = t^{2} {\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2597

\[ {}y^{\prime \prime }+y^{\prime }+y = t^{2}+t +1 \]

[[_2nd_order, _with_linear_symmetries]]

2598

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

2599

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = t^{2} {\mathrm e}^{7 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2600

\[ {}y^{\prime \prime }+4 y = t \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2601

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = \left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2602

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \cos \left (t \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2603

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \cos \left (t \right )^{2} {\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2604

\[ {}y^{\prime \prime }+y^{\prime }-6 y = \sin \left (t \right )+t \,{\mathrm e}^{2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2605

\[ {}y^{\prime \prime }+y^{\prime }+4 y = t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2606

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t}+{\mathrm e}^{2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2607

\[ {}y^{\prime \prime }+2 y^{\prime } = 1+t^{2}+{\mathrm e}^{-2 t} \]

[[_2nd_order, _missing_y]]

2608

\[ {}y^{\prime \prime }+y = \cos \left (t \right ) \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2609

\[ {}y^{\prime \prime }+y = \cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2610

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t^{{3}/{2}} {\mathrm e}^{3 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2628

\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0 \]

[[_Emden, _Fowler]]

2629

\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2630

\[ {}\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2631

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

2632

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

2633

\[ {}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2634

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2635

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

2636

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0 \]
i.c.

[[_Emden, _Fowler]]

2637

\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

2835

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2836

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2837

\[ {}y^{\prime \prime }-\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2838

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2839

\[ {}y^{\prime \prime }-2 y^{\prime }+\left (1+\lambda \right ) y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2840

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3059

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

3060

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 0 \]

[[_2nd_order, _missing_x]]

3061

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

3062

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

3063

\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

3064

\[ {}y^{\prime \prime }-2 y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

3065

\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

3066

\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

3067

\[ {}2 y^{\prime \prime }+2 y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

3088

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

3089

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

3100

\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

3111

\[ {}y^{\prime \prime }-4 y = 3 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3112

\[ {}y^{\prime \prime }+y = \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3113

\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

3114

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

3115

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3116

\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

3117

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3119

\[ {}y^{\prime \prime }-4 y = x +{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

3120

\[ {}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3121

\[ {}y^{\prime \prime }-y^{\prime }-6 y = x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3122

\[ {}-2 y^{\prime \prime }+3 y = x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3123

\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3125

\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x} \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3128

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3131

\[ {}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = 5 \cos \left (6 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3132

\[ {}y^{\prime \prime }+9 y = \left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3133

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3135

\[ {}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3137

\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3138

\[ {}y^{\prime \prime }+4 y = 12 \cos \left (x \right )^{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3139

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3140

\[ {}y^{\prime \prime }+y = {\mathrm e}^{x} \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3141

\[ {}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _missing_y]]

3142

\[ {}y^{\prime \prime }+y = 3 x \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3143

\[ {}2 y^{\prime \prime }+5 y^{\prime }-3 y = \sin \left (x \right )-8 x \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3144

\[ {}8 y^{\prime \prime }-y = x \,{\mathrm e}^{-\frac {x}{2}} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3145

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3146

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

3147

\[ {}y^{\prime \prime }+4 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

3148

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

3149

\[ {}y^{\prime \prime }+y = 4 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3150

\[ {}y^{\prime \prime }+4 y = 2 x -2 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3151

\[ {}y^{\prime \prime }-y = 3 x +5 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

3152

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{x}+\sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3155

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3156

\[ {}y^{\prime \prime }+a^{2} y = \sec \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3160

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3161

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3162

\[ {}y^{\prime \prime }+4 y = \sec \left (x \right ) \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3163

\[ {}y^{\prime \prime }-2 y = {\mathrm e}^{-x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3164

\[ {}y^{\prime \prime }+9 y = \sec \left (x \right ) \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3165

\[ {}y^{\prime \prime }+9 y = \csc \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3166

\[ {}y^{\prime \prime }+y = \tan \left (\frac {x}{3}\right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3168

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{\frac {x}{2}} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3170

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

3172

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

3173

\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

3174

\[ {}y^{\prime \prime }+3 y = 3 \,{\mathrm e}^{-4 x} \]

[[_2nd_order, _with_linear_symmetries]]

3175

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3176

\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

3177

\[ {}y^{\prime \prime }+2 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3178

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3179

\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3180

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3184

\[ {}y^{\prime \prime }+y = {\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3185

\[ {}y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y = \sin \left (k x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3186

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3187

\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3188

\[ {}y^{\prime \prime }+4 y = x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3189

\[ {}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3190

\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2}-8 \]

[[_2nd_order, _with_linear_symmetries]]

3205

\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3206

\[ {}y^{\prime \prime }+y = x^{2} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3207

\[ {}y^{\prime \prime }-y = x^{2} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3210

\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = x^{2} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3214

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3215

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3216

\[ {}y^{\prime \prime }-y = x \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3217

\[ {}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right ) \]

[[_2nd_order, _missing_y]]

3218

\[ {}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

3219

\[ {}y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3220

\[ {}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

3221

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

3222

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

3223

\[ {}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0 \]

[[_Emden, _Fowler]]

3224

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0 \]

[[_Emden, _Fowler]]

3225

\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

3226

\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right ) \]

[[_2nd_order, _with_linear_symmetries]]

3227

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

3228

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3230

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right ) \]

[[_2nd_order, _with_linear_symmetries]]

3231

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x^{2} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3232

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (-1+x \right ) \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3244

\[ {}y^{\prime \prime } = \cos \left (t \right ) \]

[[_2nd_order, _quadrature]]

3245

\[ {}y^{\prime \prime } = k^{2} y \]

[[_2nd_order, _missing_x]]

3246

\[ {}x^{\prime \prime }+k^{2} x = 0 \]

[[_2nd_order, _missing_x]]

3249

\[ {}x y^{\prime \prime } = x^{2}+1 \]

[[_2nd_order, _quadrature]]

3250

\[ {}\left (1-x \right ) y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_y]]

3251

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \]

[[_2nd_order, _missing_y]]

3253

\[ {}x y^{\prime \prime }+x = y^{\prime } \]

[[_2nd_order, _missing_y]]

3254

\[ {}x^{\prime \prime }+t x^{\prime } = t^{3} \]

[[_2nd_order, _missing_y]]

3255

\[ {}x^{2} y^{\prime \prime } = x y^{\prime }+1 \]

[[_2nd_order, _missing_y]]

3257

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 1 \]

[[_2nd_order, _missing_y]]

3266

\[ {}y^{\prime \prime } = y \]

[[_2nd_order, _missing_x]]

3272

\[ {}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

3282

\[ {}x^{\prime \prime }-k^{2} x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3484

\[ {}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3485

\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3486

\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3487

\[ {}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3488

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3489

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3490

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

3493

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

3494

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y = x^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3495

\[ {}\left (-2+x \right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

3496

\[ {}y^{\prime \prime }-y = x^{n} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3497

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3500

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3558

\[ {}y^{\prime \prime }-25 y = 0 \]

[[_2nd_order, _missing_x]]

3559

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

3560

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

3563

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

3564

\[ {}y^{\prime \prime }-9 y = 0 \]

[[_2nd_order, _missing_x]]

3565

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

3566

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

3567

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

[[_Emden, _Fowler]]

3568

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

3569

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3570

\[ {}y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y = 0 \]

[[_2nd_order, _missing_x]]

3571

\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

3572

\[ {}y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y = 0 \]

[[_2nd_order, _missing_x]]

3573

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

3574

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

3575

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

3576

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler]]

3584

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

3585

\[ {}y^{\prime \prime } = x^{n} \]

[[_2nd_order, _quadrature]]

3587

\[ {}y^{\prime \prime } = \cos \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

3589

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _quadrature]]

3590

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

3591

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0 \]

[[_Emden, _Fowler]]

3592

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3631

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x \]

[[_2nd_order, _missing_y]]

3696

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

3697

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

3698

\[ {}y^{\prime \prime }-36 y = 0 \]

[[_2nd_order, _missing_x]]

3699

\[ {}y^{\prime \prime }+4 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

3707

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

3708

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

3711

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

3712

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 4 x^{2}+5 \]

[[_2nd_order, _with_linear_symmetries]]

3716

\[ {}y^{\prime \prime }+y = 6 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

3717

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 5 x \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3718

\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3719

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

3720

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3724

\[ {}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3725

\[ {}y^{\prime \prime }-y = 9 x \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3726

\[ {}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3727

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 4 \cos \left (x \right )-2 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3728

\[ {}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3729

\[ {}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

3732

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3733

\[ {}y^{\prime \prime }+6 y = \sin \left (x \right )^{2} \cos \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3734

\[ {}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3735

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3736

\[ {}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3737

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3738

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3739

\[ {}y^{\prime \prime }+y = 3 \,{\mathrm e}^{x} \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3740

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3741

\[ {}y^{\prime \prime }-4 y = 100 x \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3742

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3743

\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3744

\[ {}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3745

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3746

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3747

\[ {}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3748

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3749

\[ {}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3750

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3751

\[ {}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3752

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3753

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3754

\[ {}y^{\prime \prime }+y = \sec \left (x \right )+4 \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3755

\[ {}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

3756

\[ {}y^{\prime \prime }-y = 2 \tanh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3757

\[ {}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \frac {{\mathrm e}^{m x}}{x^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3758

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3759

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3760

\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3761

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

3762

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3767

\[ {}y^{\prime \prime }-9 y = F \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3768

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3769

\[ {}y^{\prime \prime }+y^{\prime }-2 y = F \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3770

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = F \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3771

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 5 x \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3772

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

3773

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3774

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3775

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

3776

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3777

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3778

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3779

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3780

\[ {}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3781

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0 \]
i.c.

[[_Emden, _Fowler]]

3782

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

3797

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

3798

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

3802

\[ {}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

3803

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3804

\[ {}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

3806

\[ {}y^{\prime \prime }+4 y = \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3807

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

3808

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3809

\[ {}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4118

\[ {}y^{\prime \prime }+8 y^{\prime }+15 y = 0 \]

[[_2nd_order, _missing_x]]

4119

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

[[_2nd_order, _missing_x]]

4120

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

4121

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

4122

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

4123

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

4124

\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

4125

\[ {}y^{\prime \prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

4126

\[ {}4 y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

4127

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

4128

\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

4129

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 1 \]

[[_2nd_order, _missing_x]]

4130

\[ {}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2 \]

[[_2nd_order, _with_linear_symmetries]]

4131

\[ {}y^{\prime \prime }+y = x^{3}+x \]

[[_2nd_order, _linear, _nonhomogeneous]]

4132

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

4133

\[ {}y^{\prime \prime }+2 y = x +{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

4134

\[ {}y^{\prime \prime }+2 y = {\mathrm e}^{x}+2 \]

[[_2nd_order, _with_linear_symmetries]]

4135

\[ {}y^{\prime \prime }-y = 2 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

4136

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4137

\[ {}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4138

\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = x^{3}+\sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4139

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

4140

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}+2 \]

[[_2nd_order, _with_linear_symmetries]]

4141

\[ {}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = A \cos \left (x p \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4152

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4153

\[ {}y^{\prime \prime }+2 y^{\prime }-2 y = x^{2}+1 \]

[[_2nd_order, _with_linear_symmetries]]

4154

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8} = \frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4155

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}-2 \,{\mathrm e}^{2 x}+\sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4156

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4157

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4158

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4161

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

4162

\[ {}y^{\prime \prime }+9 y = 8 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4163

\[ {}25 y^{\prime \prime }-30 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

4164

\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = \left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4426

\[ {}x y^{\prime \prime } = y^{\prime }+x \]

[[_2nd_order, _missing_y]]

4456

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4457

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4458

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (x +{\mathrm e}^{x}\right ) \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4459

\[ {}y^{\prime \prime }+4 y = \sinh \left (x \right ) \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4460

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cosh \left (x \right ) \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4470

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 36 x \,{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4474

\[ {}y^{\prime \prime }+3 y^{\prime }+5 y = 5 \,{\mathrm e}^{-x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4476

\[ {}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4479

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \left (x +1\right ) {\mathrm e}^{x}+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4480

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 4 \,{\mathrm e}^{x} \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4481

\[ {}y^{\prime \prime }+4 y = 4 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4482

\[ {}y^{\prime \prime }-y = 12 x^{2} {\mathrm e}^{x}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4483

\[ {}y^{\prime \prime }+y = 2 \sin \left (x \right )-3 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4484

\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (x^{2}+10\right ) \]

[[_2nd_order, _missing_y]]

4485

\[ {}y^{\prime \prime }-4 y = 96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4486

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (x \right )+10 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4487

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 4 x -2+2 \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4488

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x \,{\mathrm e}^{2 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4497

\[ {}y^{\prime \prime }-y = \frac {1}{x}-\frac {2}{x^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4498

\[ {}y^{\prime \prime }-y = \frac {1}{\sinh \left (x \right )} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4499

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4500

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4501

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4502

\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4503

\[ {}y^{\prime \prime }-y = \frac {1}{\sqrt {1-{\mathrm e}^{2 x}}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4504

\[ {}y^{\prime \prime }-y = {\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4505

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 15 \,{\mathrm e}^{-x} \sqrt {x +1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4506

\[ {}y^{\prime \prime }+4 y = 2 \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

4507

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4508

\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1} \]

[[_2nd_order, _missing_y]]

4509

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

4510

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4512

\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-3 \left (-2+x \right ) y^{\prime }+4 y = x \]

[[_2nd_order, _with_linear_symmetries]]

5916

\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

5917

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

5918

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

5919

\[ {}6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

5920

\[ {}y^{\prime \prime }+2 y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

5925

\[ {}y^{\prime \prime }-2 k y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

5926

\[ {}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

5928

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

5931

\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

5937

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

5938

\[ {}y^{\prime \prime }-y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

5940

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

[[_2nd_order, _missing_x]]

5945

\[ {}y^{\prime \prime } = 0 \]
i.c.

[[_2nd_order, _quadrature]]

5946

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

5947

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

5948

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

5950

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \]

[[_2nd_order, _missing_x]]

5951

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

5952

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x} \]

[[_2nd_order, _with_linear_symmetries]]

5953

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5954

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5955

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5956

\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

5957

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5958

\[ {}y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

5959

\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+2 x \]

[[_2nd_order, _missing_y]]

5960

\[ {}y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right ) \]

[[_2nd_order, _missing_y]]

5961

\[ {}y^{\prime \prime }+y = 4 x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5962

\[ {}y^{\prime \prime }+4 y = x \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5963

\[ {}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5964

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5965

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5966

\[ {}y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

5967

\[ {}y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5968

\[ {}y^{\prime \prime }+y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5969

\[ {}y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5970

\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

5971

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

5972

\[ {}y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

5973

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

5974

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

5975

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5976

\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5977

\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5978

\[ {}y^{\prime \prime }-y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5979

\[ {}y^{\prime \prime }+y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5980

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

5981

\[ {}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5982

\[ {}y^{\prime \prime }+y = 4 x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5983

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5984

\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5985

\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5986

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

5987

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5988

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5989

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

5990

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

5991

\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = \ln \left (x \right ) x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

5992

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

5993

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

5994

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

5998

\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \]

[[_2nd_order, _missing_y]]

5999

\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \]

[[_2nd_order, _missing_y]]

6009

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \]

[[_2nd_order, _missing_y]]

6014

\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \]
i.c.

[[_2nd_order, _missing_y]]

6015

\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \]
i.c.

[[_2nd_order, _missing_y]]

6026

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

6077

\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6078

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6079

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6080

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6081

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6082

\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

6083

\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

6084

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6085

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6086

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6087

\[ {}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

6091

\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler]]

6135

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

6136

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

6137

\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

6138

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

6139

\[ {}y^{\prime \prime }-2 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

6140

\[ {}y^{\prime \prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

6141

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

6142

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

6143

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

6144

\[ {}2 y^{\prime \prime }+y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

6145

\[ {}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0 \]

[[_2nd_order, _missing_x]]

6146

\[ {}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0 \]

[[_2nd_order, _missing_x]]

6151

\[ {}y^{\prime \prime }-4 y^{\prime } = 10 \]

[[_2nd_order, _missing_x]]

6152

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 16 \]

[[_2nd_order, _missing_x]]

6153

\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6154

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6155

\[ {}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

6156

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

6157

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6158

\[ {}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

6159

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

6160

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6161

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6162

\[ {}y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6163

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6164

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6165

\[ {}5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6166

\[ {}y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6167

\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6168

\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6169

\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6170

\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6171

\[ {}5 y^{\prime \prime }+6 y^{\prime }+2 y = x^{2}+6 x \]

[[_2nd_order, _with_linear_symmetries]]

6172

\[ {}2 y^{\prime \prime }+y^{\prime } = 2 x \]

[[_2nd_order, _missing_y]]

6173

\[ {}y^{\prime \prime }+y = 2 x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6174

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6175

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6176

\[ {}y^{\prime \prime }+y = 8 x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6177

\[ {}y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6178

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5 \]

[[_2nd_order, _with_linear_symmetries]]

6179

\[ {}y^{\prime \prime }-y = \sinh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6180

\[ {}y^{\prime \prime }+y = 2 \sin \left (x \right )+4 x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6181

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6182

\[ {}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _missing_y]]

6187

\[ {}y^{\prime \prime }+2 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

6192

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \]

[[_Emden, _Fowler]]

6193

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

6194

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

6195

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+6 y = 0 \]

[[_Emden, _Fowler]]

6196

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \]

[[_2nd_order, _with_linear_symmetries]]

6197

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

6198

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

6199

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 x^{2} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6200

\[ {}x^{2} y^{\prime \prime }+y = 3 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

6201

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x \]

[[_2nd_order, _with_linear_symmetries]]

6211

\[ {}r^{\prime \prime }-6 r^{\prime }+9 r = 0 \]

[[_2nd_order, _missing_x]]

6213

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6215

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

6219

\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \]

[[_2nd_order, _missing_y]]

6220

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6221

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6222

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 6 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6223

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6227

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6234

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 6 \]
i.c.

[[_2nd_order, _missing_x]]

6243

\[ {}y^{\prime \prime } = -4 y \]

[[_2nd_order, _missing_x]]

6245

\[ {}y^{\prime \prime } = y \]

[[_2nd_order, _missing_x]]

6247

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

6249

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \]

[[_Emden, _Fowler]]

6251

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6253

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6255

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6388

\[ {}x^{\prime \prime }-\omega ^{2} x = 0 \]

[[_2nd_order, _missing_x]]

6390

\[ {}x^{\prime \prime }+42 x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6393

\[ {}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6394

\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

6395

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6396

\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6397

\[ {}y^{\prime \prime }-y = \cosh \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6407

\[ {}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6408

\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

6409

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

6410

\[ {}x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

6411

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

6412

\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

6413

\[ {}x y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6414

\[ {}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6479

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 8 \]

[[_2nd_order, _missing_x]]

6480

\[ {}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6481

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6482

\[ {}y^{\prime \prime }+25 y = 5 x^{2}+x \]

[[_2nd_order, _with_linear_symmetries]]

6483

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6484

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

6485

\[ {}3 y^{\prime \prime }-2 y^{\prime }-y = 2 x -3 \]

[[_2nd_order, _with_linear_symmetries]]

6486

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

6487

\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6488

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

[[_2nd_order, _with_linear_symmetries]]

6489

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6490

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \sinh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6491

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 2 \cosh \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6492

\[ {}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6493

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \cos \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6494

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x +{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6495

\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1 \]

[[_2nd_order, _with_linear_symmetries]]

6496

\[ {}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6497

\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

6498

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6499

\[ {}x^{\prime \prime }-3 x^{\prime }+2 x = \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6500

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 3 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6501

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

[[_2nd_order, _with_linear_symmetries]]

6502

\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6503

\[ {}y^{\prime \prime } = 3 \sin \left (x \right )-4 y \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6504

\[ {}\frac {x^{\prime \prime }}{2} = -48 x \]
i.c.

[[_2nd_order, _missing_x]]

6505

\[ {}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

6506

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

6507

\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6508

\[ {}y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6509

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6510

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

6511

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

[[_2nd_order, _linear, _nonhomogeneous]]

6513

\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \]

[[_2nd_order, _quadrature]]

6514

\[ {}y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

6518

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1 \]

[[_2nd_order, _with_linear_symmetries]]

6519

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6520

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6521

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

6522

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6529

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6530

\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6531

\[ {}x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6532

\[ {}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right ) \]

[[_2nd_order, _with_linear_symmetries]]

6535

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6536

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6537

\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6538

\[ {}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

[[_2nd_order, _with_linear_symmetries]]

6539

\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \]

[[_2nd_order, _missing_x]]

6540

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

6541

\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = x^{3} {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

6573

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

6574

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6575

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

6576

\[ {}y^{\prime \prime }-y = 4-x \]

[[_2nd_order, _with_linear_symmetries]]

6577

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

6578

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \left (1-x \right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6691

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

6693

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

6694

\[ {}y^{\prime \prime }+9 y = x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6695

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

6697

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

6701

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

[[_2nd_order, _missing_x]]

6703

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

6705

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

6706

\[ {}y^{\prime \prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

6711

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 1 \]

[[_2nd_order, _missing_x]]

6712

\[ {}y^{\prime \prime }-4 y^{\prime } = 5 \]

[[_2nd_order, _missing_x]]

6716

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

6717

\[ {}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2 \]

[[_2nd_order, _with_linear_symmetries]]

6718

\[ {}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6719

\[ {}y^{\prime \prime }-y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6720

\[ {}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6721

\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6722

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6723

\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6724

\[ {}y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6725

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6726

\[ {}y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6727

\[ {}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6728

\[ {}y^{\prime \prime }+2 y = {\mathrm e}^{x}+2 \]

[[_2nd_order, _with_linear_symmetries]]

6729

\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6730

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6731

\[ {}y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6733

\[ {}y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6735

\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \]

[[_2nd_order, _linear, _nonhomogeneous]]

6736

\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

6737

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+x \,{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6740

\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6741

\[ {}y^{\prime \prime }+5 y = \cos \left (\sqrt {5}\, x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6743

\[ {}y^{\prime \prime }-y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

6744

\[ {}y^{\prime \prime }+2 y = x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6745

\[ {}y^{\prime \prime }-2 y^{\prime }-y = {\mathrm e}^{x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6746

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6747

\[ {}y^{\prime \prime }-y = x \,{\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6748

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6749

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +x^{2} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6750

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \]

[[_2nd_order, _with_linear_symmetries]]

6753

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = \ln \left (x +1\right )^{2}+x -1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

6754

\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

6755

\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \]

[_Laguerre]

6756

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 2 \]

[[_2nd_order, _with_linear_symmetries]]

6757

\[ {}\left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8 \]

[[_2nd_order, _with_linear_symmetries]]

6758

\[ {}\left (x +1\right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (2+x \right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6759

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6760

\[ {}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6761

\[ {}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6762

\[ {}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6763

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

6764

\[ {}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {x +1}{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6765

\[ {}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

6767

\[ {}x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = 2+x \]

[[_2nd_order, _with_linear_symmetries]]

6768

\[ {}\left (x +1\right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (3 x +2\right ) {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

6769

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6770

\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 4 \]

[[_2nd_order, _linear, _nonhomogeneous]]

6771

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \frac {-x^{2}+1}{x} \]

[[_2nd_order, _with_linear_symmetries]]

6773

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}} \]

[[_2nd_order, _missing_y]]

6774

\[ {}x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right ) \]

[[_2nd_order, _missing_y]]

6888

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

6889

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6898

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

6908

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

6909

\[ {}2 y^{\prime \prime }+7 y^{\prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

6910

\[ {}x y^{\prime \prime }+2 y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

6911

\[ {}4 x^{2} y^{\prime \prime }+y = 0 \]

[[_Emden, _Fowler]]

6912

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

[[_Emden, _Fowler]]

6917

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = 10 \]

[[_2nd_order, _missing_x]]

6925

\[ {}y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6927

\[ {}y^{\prime \prime } = f \left (x \right ) \]

[[_2nd_order, _quadrature]]

6939

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6940

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6941

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6942

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6943

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6944

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6945

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6946

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6972

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6973

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6974

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6975

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6986

\[ {}y^{\prime \prime }+9 y = 18 \]

[[_2nd_order, _missing_x]]

6987

\[ {}x y^{\prime \prime }-y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

6988

\[ {}y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

6996

\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right )-2 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6997

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

6998

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

6999

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \sec \left (\ln \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7002

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7003

\[ {}y^{\prime \prime }+y = {\mathrm e}^{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7008

\[ {}y^{\prime \prime }+9 y = 5 \]

[[_2nd_order, _missing_x]]

7010

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7011

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7012

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7013

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

7478

\[ {}y^{\prime \prime }+2 y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

7479

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

7480

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7483

\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7484

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

7487

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler]]

7489

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7490

\[ {}y^{\prime \prime }+x y^{\prime }+y = 2 x \,{\mathrm e}^{x}-1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

7491

\[ {}x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \]

[[_2nd_order, _with_linear_symmetries]]

7492

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

7493

\[ {}x^{3} y^{\prime \prime }+x y^{\prime }-y = \cos \left (\frac {1}{x}\right ) \]

[[_2nd_order, _with_linear_symmetries]]

7494

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y = x +\frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

7495

\[ {}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = x^{2}-1 \]

[[_2nd_order, _with_linear_symmetries]]

7498

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7499

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7517

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

7518

\[ {}s^{\prime \prime }+2 s^{\prime }+s = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7519

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

7520

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 3 x +1 \]

[[_2nd_order, _with_linear_symmetries]]

7521

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7522

\[ {}y^{\prime \prime }+y = 4 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7523

\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7524

\[ {}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7525

\[ {}\sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u = 0 \]

[_Lienard]

7527

\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7535

\[ {}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7536

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

7537

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

7538

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7540

\[ {}y^{\prime \prime }+4 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

7541

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7542

\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7545

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7546

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7557

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7581

\[ {}y^{\prime \prime } = 2+x \]

[[_2nd_order, _quadrature]]

7585

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

7586

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

7587

\[ {}y^{\prime \prime }+k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

7589

\[ {}y^{\prime \prime } = 3 x +1 \]

[[_2nd_order, _quadrature]]

7612

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

7613

\[ {}3 y^{\prime \prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

7614

\[ {}y^{\prime \prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

7615

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

7616

\[ {}y^{\prime \prime }+2 i y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

7617

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

7618

\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

[[_2nd_order, _missing_x]]

7619

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7620

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7621

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7622

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7623

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7624

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7625

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7626

\[ {}y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7627

\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7628

\[ {}y^{\prime \prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7629

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7630

\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7631

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7632

\[ {}y^{\prime \prime }+2 i y^{\prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

7633

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7634

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7635

\[ {}y^{\prime \prime }+y = 2 \sin \left (2 x \right ) \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7636

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7637

\[ {}4 y^{\prime \prime }-y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

7638

\[ {}6 y^{\prime \prime }+5 y^{\prime }-6 y = x \]

[[_2nd_order, _with_linear_symmetries]]

7639

\[ {}y^{\prime \prime }+\omega ^{2} y = A \cos \left (\omega x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

7650

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

7651

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

7657

\[ {}y^{\prime \prime }-2 i y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

7664

\[ {}y^{\prime \prime }-2 i y^{\prime }-y = {\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7665

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7666

\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7667

\[ {}y^{\prime \prime }-4 y = 3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7668

\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2}+\cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7669

\[ {}y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7670

\[ {}y^{\prime \prime }+y = x \,{\mathrm e}^{x} \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7671

\[ {}y^{\prime \prime }+i y^{\prime }+2 y = 2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7674

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

7675

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

7676

\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

7686

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

7697

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7699

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7700

\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_Emden, _Fowler]]

7701

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7702

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

7704

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

7705

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

7706

\[ {}x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0 \]

[[_Emden, _Fowler]]

7707

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y = x \]

[[_2nd_order, _with_linear_symmetries]]

7759

\[ {}y^{\prime \prime }+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

7762

\[ {}y^{\prime \prime }+k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

7764

\[ {}x y^{\prime \prime }-2 y^{\prime } = x^{3} \]

[[_2nd_order, _missing_y]]

7777

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

7778

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

7804

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

7907

\[ {}y^{\prime \prime }-k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

7911

\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \]

[[_2nd_order, _missing_y]]

7936

\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \]

[[_2nd_order, _missing_y]]

7937

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

7938

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

7939

\[ {}y^{\prime \prime }+8 y = 0 \]

[[_2nd_order, _missing_x]]

7940

\[ {}2 y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

7941

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

7942

\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 0 \]

[[_2nd_order, _missing_x]]

7943

\[ {}2 y^{\prime \prime }+2 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

7944

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

7945

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

7946

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

7947

\[ {}4 y^{\prime \prime }+20 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

7948

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

7949

\[ {}y^{\prime \prime } = 4 y \]

[[_2nd_order, _missing_x]]

7950

\[ {}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \]

[[_2nd_order, _missing_x]]

7951

\[ {}2 y^{\prime \prime }+y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

7952

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

7953

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

7954

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 0 \]

[[_2nd_order, _missing_x]]

7955

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7956

\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7957

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7958

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7959

\[ {}y^{\prime \prime }+4 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7960

\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7961

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

[[_Emden, _Fowler]]

7962

\[ {}2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

[[_Emden, _Fowler]]

7963

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

[[_Emden, _Fowler]]

7964

\[ {}4 x^{2} y^{\prime \prime }-3 y = 0 \]

[[_Emden, _Fowler]]

7965

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7966

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7967

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y = 0 \]

[[_Emden, _Fowler]]

7968

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7969

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

7970

\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

7971

\[ {}y^{\prime \prime }+4 y = 3 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7972

\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \]

[[_2nd_order, _with_linear_symmetries]]

7973

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \]

[[_2nd_order, _with_linear_symmetries]]

7974

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

7975

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7976

\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7977

\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

[[_2nd_order, _missing_y]]

7978

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

7979

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7980

\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

[[_2nd_order, _missing_y]]

7981

\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \]

[[_2nd_order, _linear, _nonhomogeneous]]

7982

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7983

\[ {}y^{\prime \prime }-3 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

7985

\[ {}y^{\prime \prime }+4 y = \tan \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7986

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7987

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7988

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7989

\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

7990

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7991

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7992

\[ {}y^{\prime \prime }+y = \cot \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

7993

\[ {}y^{\prime \prime }+y = \cot \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7994

\[ {}y^{\prime \prime }+y = x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7995

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7996

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7997

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

7998

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \]

[[_2nd_order, _with_linear_symmetries]]

7999

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

8000

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

8001

\[ {}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y = x \left (x +1\right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

8002

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

8003

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

8004

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

8039

\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

8040

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

8041

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

8042

\[ {}y^{\prime \prime }-y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

8043

\[ {}y^{\prime \prime }-2 y^{\prime }-5 y = x \]

[[_2nd_order, _with_linear_symmetries]]

8044

\[ {}y^{\prime \prime }+y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

8045

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8046

\[ {}y^{\prime \prime }-y = {\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

8047

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8048

\[ {}y^{\prime \prime }-y^{\prime }+4 y = x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8049

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8050

\[ {}y^{\prime \prime }+3 y^{\prime }+4 y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8051

\[ {}y^{\prime \prime }+y = {\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8052

\[ {}y^{\prime \prime }-y = \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8053

\[ {}y^{\prime \prime } = \tan \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

8054

\[ {}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right ) \]
i.c.

[[_2nd_order, _missing_y]]

8055

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1 \]

[[_2nd_order, _with_linear_symmetries]]

8056

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

8057

\[ {}y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8058

\[ {}y^{\prime \prime }+2 y^{\prime }-y = x \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8059

\[ {}y^{\prime \prime }+9 y = \sec \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8060

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \ln \left (x \right ) x \]

[[_2nd_order, _linear, _nonhomogeneous]]

8061

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

8062

\[ {}y^{\prime \prime }+4 y = \tan \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

8067

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

8068

\[ {}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8070

\[ {}y^{\prime \prime } = -3 y \]
i.c.

[[_2nd_order, _missing_x]]

8219

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

8221

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

8223

\[ {}y^{\prime \prime }-y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

8225

\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

8289

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8294

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8301

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8303

\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \]

[[_Emden, _Fowler]]

8307

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

8308

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8309

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8310

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8362

\[ {}t y^{\prime \prime }-y^{\prime } = 2 t^{2} \]
i.c.

[[_2nd_order, _missing_y]]

8363

\[ {}2 y^{\prime \prime }+t y^{\prime }-2 y = 10 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8496

\[ {}x y^{\prime \prime } = y^{\prime }+x^{5} \]
i.c.

[[_2nd_order, _missing_y]]

8497

\[ {}x y^{\prime \prime }+y^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_y]]

8500

\[ {}y^{\prime \prime }+\beta ^{2} y = 0 \]

[[_2nd_order, _missing_x]]

8509

\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3 \]

[[_2nd_order, _missing_y]]

8529

\[ {}y^{\prime \prime }+y = -\cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8530

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

8531

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

8532

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1 \]

[[_2nd_order, _with_linear_symmetries]]

8606

\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_Emden, _Fowler]]

8607

\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

8608

\[ {}9 x^{2} y^{\prime \prime }+2 y = 0 \]

[[_Emden, _Fowler]]

8609

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

8610

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

[[_Emden, _Fowler]]

8611

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

8612

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

8613

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

8614

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

8705

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

8706

\[ {}y^{\prime \prime }+16 y = 4 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8707

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

8708

\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

8752

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

8753

\[ {}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8754

\[ {}y^{\prime \prime }+y^{\prime }+4 y = 1 \]

[[_2nd_order, _missing_x]]

8755

\[ {}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8759

\[ {}t y^{\prime \prime }+4 y^{\prime } = t^{2} \]

[[_2nd_order, _missing_y]]

8760

\[ {}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_y]]

8761

\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

8762

\[ {}t y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

8763

\[ {}t^{2} y^{\prime \prime }-2 y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

8765

\[ {}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

8766

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

8767

\[ {}y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

8768

\[ {}y^{\prime \prime } = f \left (t \right ) \]

[[_2nd_order, _quadrature]]

8769

\[ {}y^{\prime \prime } = k \]

[[_2nd_order, _quadrature]]

8772

\[ {}y^{\prime \prime } = 4 \sin \left (x \right )-4 \]

[[_2nd_order, _quadrature]]

8795

\[ {}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

8800

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8801

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8802

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8805

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8806

\[ {}y^{\prime \prime }-x y^{\prime }-x y-2 x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8807

\[ {}y^{\prime \prime }-x y^{\prime }-x y-3 x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8808

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8809

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

8810

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

8811

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

8812

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8813

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8814

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

8848

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8853

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8859

\[ {}y^{\prime \prime }+c y^{\prime }+k y = 0 \]

[[_2nd_order, _missing_x]]

8861

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8862

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8863

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8864

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8865

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8866

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8867

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8868

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8869

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8870

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8871

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8873

\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

8874

\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x \]

[[_2nd_order, _with_linear_symmetries]]

8875

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x \]

[[_2nd_order, _with_linear_symmetries]]

8888

\[ {}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8957

\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

8960

\[ {}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8963

\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8964

\[ {}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8965

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

8966

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

8967

\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 6 x^{3} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

8977

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (2+x \right ) {\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

8981

\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9072

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

9075

\[ {}a y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

9078

\[ {}y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

9080

\[ {}y^{\prime \prime } = x \]

[[_2nd_order, _quadrature]]

9083

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

9086

\[ {}y^{\prime \prime }+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

9089

\[ {}y^{\prime \prime }+y^{\prime } = x \]

[[_2nd_order, _missing_y]]

9092

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

9095

\[ {}y^{\prime \prime }+y^{\prime }+y = 1 \]

[[_2nd_order, _missing_x]]

9096

\[ {}y^{\prime \prime }+y^{\prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

9097

\[ {}y^{\prime \prime }+y^{\prime }+y = x +1 \]

[[_2nd_order, _with_linear_symmetries]]

9098

\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2}+x +1 \]

[[_2nd_order, _with_linear_symmetries]]

9099

\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

9100

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

9101

\[ {}y^{\prime \prime }+y^{\prime }+y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

9102

\[ {}y^{\prime \prime }+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

9103

\[ {}y^{\prime \prime }+y^{\prime } = x \]

[[_2nd_order, _missing_y]]

9104

\[ {}y^{\prime \prime }+y^{\prime } = x +1 \]

[[_2nd_order, _missing_y]]

9105

\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+x +1 \]

[[_2nd_order, _missing_y]]

9106

\[ {}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \]

[[_2nd_order, _missing_y]]

9107

\[ {}y^{\prime \prime }+y^{\prime } = \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

9108

\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right ) \]

[[_2nd_order, _missing_y]]

9109

\[ {}y^{\prime \prime }+y = 1 \]

[[_2nd_order, _missing_x]]

9110

\[ {}y^{\prime \prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

9111

\[ {}y^{\prime \prime }+y = x +1 \]

[[_2nd_order, _with_linear_symmetries]]

9112

\[ {}y^{\prime \prime }+y = x^{2}+x +1 \]

[[_2nd_order, _with_linear_symmetries]]

9113

\[ {}y^{\prime \prime }+y = x^{3}+x^{2}+x +1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

9114

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

9115

\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

9137

\[ {}y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

9138

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = x \]

[[_2nd_order, _linear, _nonhomogeneous]]

9139

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9140

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-c^{2} y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9142

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{3}-x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

9146

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

9147

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5} \]

[[_2nd_order, _linear, _nonhomogeneous]]

9150

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x^{m +1} \]

[[_2nd_order, _with_linear_symmetries]]

9151

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9153

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

9154

\[ {}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x \]

[[_2nd_order, _linear, _nonhomogeneous]]

9155

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

9156

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

9157

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 \left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9158

\[ {}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9160

\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9161

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9169

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9173

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

9174

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

9175

\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9176

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

9177

\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9178

\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9179

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9180

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9181

\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9182

\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9183

\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9184

\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9185

\[ {}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9186

\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

9187

\[ {}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9188

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9189

\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

9190

\[ {}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9191

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9192

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9193

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9194

\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9195

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9196

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9197

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9198

\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9199

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9200

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9201

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9202

\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9203

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9204

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9205

\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9206

\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9207

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9208

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9209

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9210

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9211

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9212

\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9213

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9214

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9215

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9216

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9217

\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9218

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9219

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9220

\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9221

\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9222

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9223

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9224

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9225

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \]

[_Gegenbauer]

9226

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9227

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \]

[_Gegenbauer]

9228

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9229

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9230

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9231

\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9232

\[ {}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9233

\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9234

\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9235

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9236

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9237

\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9238

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9239

\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9240

\[ {}\left (3 x +1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9241

\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9242

\[ {}\left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9243

\[ {}\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9244

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9245

\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9246

\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9247

\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9248

\[ {}y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9249

\[ {}\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9250

\[ {}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9251

\[ {}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9252

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9253

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9254

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9255

\[ {}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9256

\[ {}12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9257

\[ {}x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9258

\[ {}18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9259

\[ {}2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9260

\[ {}2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9261

\[ {}3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9262

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9263

\[ {}3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9264

\[ {}2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9265

\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9266

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9267

\[ {}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9268

\[ {}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9269

\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9270

\[ {}x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9271

\[ {}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9272

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9273

\[ {}x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

9274

\[ {}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9275

\[ {}3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9276

\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9277

\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9278

\[ {}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9279

\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

9280

\[ {}2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9281

\[ {}9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9282

\[ {}6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9283

\[ {}9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9284

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9285

\[ {}8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9286

\[ {}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9287

\[ {}6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9288

\[ {}28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9289

\[ {}8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9290

\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9291

\[ {}3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9292

\[ {}4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9293

\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9294

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9295

\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9296

\[ {}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9297

\[ {}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9298

\[ {}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9299

\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9300

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9301

\[ {}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9302

\[ {}9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9303

\[ {}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9304

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9305

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9306

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9307

\[ {}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9308

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (4+3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9309

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9310

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9311

\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9312

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9313

\[ {}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9314

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9315

\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9316

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9317

\[ {}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9318

\[ {}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9319

\[ {}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9320

\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9321

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9322

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9323

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9324

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9325

\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9326

\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

9327

\[ {}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9328

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9329

\[ {}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9330

\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9331

\[ {}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9332

\[ {}x^{2} \left (4+3 x \right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9333

\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9334

\[ {}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9335

\[ {}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9336

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9337

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9338

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9339

\[ {}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9340

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9341

\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9342

\[ {}x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9343

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9344

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9345

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9346

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9347

\[ {}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9348

\[ {}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9349

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9350

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9351

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9352

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9353

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9354

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9355

\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9356

\[ {}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9357

\[ {}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9358

\[ {}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9359

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9360

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9361

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9362

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9363

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9364

\[ {}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9365

\[ {}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9366

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \]

[_Gegenbauer]

9367

\[ {}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9368

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \]

[_Gegenbauer]

9369

\[ {}\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9370

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9371

\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9372

\[ {}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9373

\[ {}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0 \]

[_Laguerre]

9374

\[ {}2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9375

\[ {}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9376

\[ {}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9377

\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9378

\[ {}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0 \]

[_Lienard]

9379

\[ {}t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9380

\[ {}t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0 \]

[_Laguerre]

9381

\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9382

\[ {}t y^{\prime \prime }+t y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9383

\[ {}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9384

\[ {}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9385

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9386

\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y = 0 \]

[_Gegenbauer]

9387

\[ {}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9388

\[ {}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9389

\[ {}z y^{\prime \prime }-2 y^{\prime }+y z = 0 \]

[_Lienard]

9390

\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9391

\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \]

[_erf]

9392

\[ {}y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9393

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9394

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \]

[_Gegenbauer]

9395

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

9396

\[ {}y^{\prime \prime }+x y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9397

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9398

\[ {}4 y^{\prime \prime }+x y^{\prime }+4 y = 0 \]

[_Lienard]

9399

\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9400

\[ {}4 x y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9401

\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9402

\[ {}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9403

\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9404

\[ {}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9405

\[ {}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9406

\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9407

\[ {}x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9408

\[ {}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9409

\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9410

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9411

\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9412

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9413

\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9414

\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9415

\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9416

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9417

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9418

\[ {}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9419

\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9420

\[ {}x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9421

\[ {}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9422

\[ {}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9423

\[ {}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9424

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9425

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9426

\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9427

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9428

\[ {}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9429

\[ {}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9430

\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9431

\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9432

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9433

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9434

\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {x y^{\prime }}{2}-\frac {3 x y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9435

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9436

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9437

\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9438

\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9439

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0 \]

[_Jacobi]

9440

\[ {}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9441

\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \]

[_Jacobi]

9442

\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \]

[_Jacobi]

9443

\[ {}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9444

\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9445

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9446

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9447

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9448

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9449

\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

9450

\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

9451

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9452

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9453

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9454

\[ {}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

9455

\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler]]

9456

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9457

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9458

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9459

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9460

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9461

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9462

\[ {}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9463

\[ {}y^{\prime \prime }-x y^{\prime }-3 y = 0 \]

[_Hermite]

9464

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9465

\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[_Hermite]

9466

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9467

\[ {}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9468

\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

9469

\[ {}x y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9470

\[ {}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9471

\[ {}y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9472

\[ {}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9473

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9474

\[ {}2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9475

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9476

\[ {}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9477

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9478

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

9479

\[ {}x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9480

\[ {}x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9481

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9482

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9483

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9484

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9485

\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[_Hermite]

9486

\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9487

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \]

[[_Emden, _Fowler]]

9488

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9489

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9490

\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9491

\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

9492

\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \]

[_Laguerre]

9493

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9494

\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9495

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9496

\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9497

\[ {}x^{4} y^{\prime \prime }+\lambda y = 0 \]

[[_Emden, _Fowler]]

9498

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9499

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9500

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9501

\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \]

[[_Emden, _Fowler]]

9502

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9503

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9504

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9505

\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \]

[_Laguerre]

9506

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9507

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

9508

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9509

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]

[_Gegenbauer]

9510

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9511

\[ {}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9512

\[ {}2 x \left (-1+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Jacobi]

9513

\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9514

\[ {}x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9515

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9516

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9517

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \]

[_Jacobi]

9518

\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9519

\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9520

\[ {}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9521

\[ {}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9522

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9523

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9524

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

9525

\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler]]

9526

\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9527

\[ {}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9528

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9529

\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9530

\[ {}u^{\prime \prime }+\frac {u}{x^{2}} = 0 \]

[[_Emden, _Fowler]]

9531

\[ {}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9532

\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9533

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9534

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9535

\[ {}y^{\prime \prime }+\frac {y}{2 x^{4}} = 0 \]

[[_Emden, _Fowler]]

9536

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9537

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9538

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9539

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9540

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9541

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9542

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9543

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9544

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9545

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9546

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9547

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9548

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0 \]

[[_Emden, _Fowler]]

9549

\[ {}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9550

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9551

\[ {}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9552

\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9553

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9554

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9555

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9556

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9557

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9558

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0 \]

[[_Emden, _Fowler]]

9559

\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

9560

\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9561

\[ {}x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9562

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9563

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9564

\[ {}y^{\prime \prime }-y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

9565

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

9566

\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9567

\[ {}\left (x +1\right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9568

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[_Gegenbauer]

9569

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

9570

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9571

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

9572

\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9573

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

9574

\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9575

\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9576

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9577

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9578

\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9579

\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9580

\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9581

\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9582

\[ {}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9583

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9584

\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9585

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9586

\[ {}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9587

\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

9588

\[ {}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9589

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9590

\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

9591

\[ {}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9592

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9593

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9594

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9595

\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9596

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9597

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9598

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9599

\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9600

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9601

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9602

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9603

\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9604

\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9605

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9606

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9607

\[ {}x^{2} y^{\prime \prime }+2 x \left (-1+x \right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9608

\[ {}x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9609

\[ {}\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9610

\[ {}2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9611

\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9612

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9613

\[ {}x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9614

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9615

\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9616

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9617

\[ {}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9618

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9619

\[ {}\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9620

\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9621

\[ {}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9622

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9623

\[ {}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9624

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9625

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9626

\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9627

\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9628

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9629

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9630

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9631

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9632

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9633

\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9634

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9635

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9636

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9637

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9638

\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9639

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9640

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9641

\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9642

\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9643

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9644

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9645

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9646

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \]

[_Gegenbauer]

9647

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9648

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \]

[_Gegenbauer]

9649

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9650

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9651

\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9652

\[ {}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9653

\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9654

\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9655

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9656

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9657

\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9658

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9659

\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9660

\[ {}\left (3 x +1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9661

\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9662

\[ {}\left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9663

\[ {}\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9664

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9665

\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9666

\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9667

\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9668

\[ {}y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9669

\[ {}\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9670

\[ {}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9671

\[ {}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9672

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9673

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9674

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9675

\[ {}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9676

\[ {}12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9677

\[ {}y^{\prime \prime }+3 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

9678

\[ {}18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9679

\[ {}2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9680

\[ {}2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9681

\[ {}3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9682

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9683

\[ {}3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9684

\[ {}2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9685

\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9686

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9687

\[ {}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9688

\[ {}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9689

\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9690

\[ {}x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9691

\[ {}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9692

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9693

\[ {}x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

9694

\[ {}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9695

\[ {}3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9696

\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9697

\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9698

\[ {}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9699

\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

9700

\[ {}2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9701

\[ {}9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9702

\[ {}6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9703

\[ {}9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9704

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9705

\[ {}8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9706

\[ {}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9707

\[ {}6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9708

\[ {}28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9709

\[ {}8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9710

\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9711

\[ {}3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9712

\[ {}4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9713

\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9714

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9715

\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9716

\[ {}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9717

\[ {}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9718

\[ {}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9719

\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9720

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9721

\[ {}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9722

\[ {}9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9723

\[ {}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9724

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9725

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9726

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9727

\[ {}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9728

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (4+3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9729

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9730

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9731

\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9732

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9733

\[ {}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9734

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9735

\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9736

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9737

\[ {}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9738

\[ {}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9739

\[ {}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9740

\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9741

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9742

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9743

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9744

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9745

\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9746

\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

9747

\[ {}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9748

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9749

\[ {}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9750

\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9751

\[ {}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9752

\[ {}x^{2} \left (4+3 x \right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9753

\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9754

\[ {}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9755

\[ {}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9756

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9757

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9758

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9759

\[ {}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9760

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9761

\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9762

\[ {}x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9763

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9764

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9765

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9766

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9767

\[ {}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9768

\[ {}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9769

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9770

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9771

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9772

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9773

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9774

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9775

\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9776

\[ {}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9777

\[ {}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9778

\[ {}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9779

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9780

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9781

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9782

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9783

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9784

\[ {}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9785

\[ {}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9786

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \]

[_Gegenbauer]

9787

\[ {}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9788

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \]

[_Gegenbauer]

9789

\[ {}\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9790

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9791

\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9792

\[ {}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9793

\[ {}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0 \]

[_Laguerre]

9794

\[ {}2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9795

\[ {}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9796

\[ {}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9797

\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9798

\[ {}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0 \]

[_Lienard]

9799

\[ {}t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9800

\[ {}t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0 \]

[_Laguerre]

9801

\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9802

\[ {}t y^{\prime \prime }+t y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9803

\[ {}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9804

\[ {}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9805

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9806

\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y = 0 \]

[_Gegenbauer]

9807

\[ {}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9808

\[ {}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9809

\[ {}z y^{\prime \prime }-2 y^{\prime }+y z = 0 \]

[_Lienard]

9810

\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9811

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9812

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9813

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

9814

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9815

\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9816

\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \]

[_erf]

9817

\[ {}y^{\prime \prime }+x y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9818

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9819

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \]

[_Gegenbauer]

9820

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

9821

\[ {}y^{\prime \prime }+x y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9822

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9823

\[ {}4 y^{\prime \prime }+x y^{\prime }+4 y = 0 \]

[_Lienard]

9824

\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9825

\[ {}4 x y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9826

\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9827

\[ {}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9828

\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9829

\[ {}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9830

\[ {}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9831

\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9832

\[ {}x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9833

\[ {}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9834

\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9835

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9836

\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9837

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9838

\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9839

\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9840

\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9841

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9842

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9843

\[ {}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9844

\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9845

\[ {}x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9846

\[ {}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9847

\[ {}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9848

\[ {}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9849

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9850

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9851

\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9852

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9853

\[ {}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9854

\[ {}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9855

\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9856

\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9857

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9858

\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9859

\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 x y}{16} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9860

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9861

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9862

\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9863

\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9864

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0 \]

[_Jacobi]

9865

\[ {}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9866

\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \]

[_Jacobi]

9867

\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \]

[_Jacobi]

9868

\[ {}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9869

\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9870

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9871

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9872

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9873

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9874

\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

9875

\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

9876

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9877

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9878

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9879

\[ {}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

9880

\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler]]

9881

\[ {}x^{2} \left (2-x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9882

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9883

\[ {}x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9884

\[ {}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9885

\[ {}x \left (x +1\right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9886

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9887

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9888

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9889

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9890

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9891

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9892

\[ {}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9893

\[ {}y^{\prime \prime }-x y^{\prime }-3 y = 0 \]

[_Hermite]

9894

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9895

\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[_Hermite]

9896

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9897

\[ {}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9898

\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

9899

\[ {}x y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9900

\[ {}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9901

\[ {}y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9902

\[ {}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9903

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9904

\[ {}2 x^{2} \left (2-x \right ) y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9905

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9906

\[ {}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9907

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

9908

\[ {}x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9909

\[ {}x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9910

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9911

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9912

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9913

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9914

\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[_Hermite]

9915

\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9916

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \]

[[_Emden, _Fowler]]

9917

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9918

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9919

\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9920

\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

9921

\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \]

[_Laguerre]

9922

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9923

\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9924

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9925

\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9926

\[ {}x^{4} y^{\prime \prime }+\lambda y = 0 \]

[[_Emden, _Fowler]]

9927

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9928

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9929

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9930

\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \]

[[_Emden, _Fowler]]

9931

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9932

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9933

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9934

\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \]

[_Laguerre]

9935

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9936

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

9937

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9938

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]

[_Gegenbauer]

9939

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9940

\[ {}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9941

\[ {}2 x \left (-1+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Jacobi]

9942

\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9943

\[ {}x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9944

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9945

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9946

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \]

[_Jacobi]

9947

\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9948

\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9949

\[ {}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9950

\[ {}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9951

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9952

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9953

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

9954

\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler]]

9955

\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9956

\[ {}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9957

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9958

\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9959

\[ {}u^{\prime \prime }+2 u^{\prime }+u = 0 \]

[[_2nd_order, _missing_x]]

9960

\[ {}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9961

\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9962

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9963

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9964

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9965

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9966

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9967

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9968

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9969

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9970

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9971

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9972

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9973

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9974

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9975

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

9976

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0 \]

[[_Emden, _Fowler]]

9977

\[ {}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9978

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9979

\[ {}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9980

\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9981

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9982

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9983

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9984

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9985

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9986

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0 \]

[[_Emden, _Fowler]]

9987

\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

9988

\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9989

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9990

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9991

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

9992

\[ {}y^{\prime \prime } = \frac {2 y}{x^{2}} \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

9993

\[ {}y^{\prime \prime } = \frac {6 y}{x^{2}} \]

[[_Emden, _Fowler]]

9994

\[ {}y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (-1+x \right )^{2}}+\frac {3}{16 x \left (-1+x \right )}\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

9995

\[ {}y^{\prime \prime } = \frac {20 y}{x^{2}} \]

[[_Emden, _Fowler]]

9996

\[ {}y^{\prime \prime } = \frac {12 y}{x^{2}} \]

[[_Emden, _Fowler]]

9997

\[ {}y^{\prime \prime }-\frac {y}{4 x^{2}} = 0 \]

[[_Emden, _Fowler]]

9998

\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

9999

\[ {}y^{\prime \prime }+\frac {y}{x^{2}} = 0 \]

[[_Emden, _Fowler]]

10000

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

10001

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

10002

\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

10003

\[ {}y^{\prime \prime } = \frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

10004

\[ {}y^{\prime \prime } = \left (\frac {6}{x^{2}}-1\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

10005

\[ {}y^{\prime \prime } = \left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

10006

\[ {}y^{\prime \prime } = \left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

10007

\[ {}y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (-1+x \right )^{2}}+\frac {3}{16 x \left (-1+x \right )}\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

10008

\[ {}y^{\prime \prime } = -\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

10009

\[ {}y^{\prime \prime } = -\frac {y}{4 x^{2}} \]

[[_Emden, _Fowler]]

10010

\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

10011

\[ {}x^{2} y^{\prime \prime } = 2 y \]

[[_2nd_order, _exact, _linear, _homogeneous]]

10012

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

10013

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

10014

\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

10997

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

10998

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

10999

\[ {}y^{\prime \prime }+y-\sin \left (n x \right ) = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11000

\[ {}y^{\prime \prime }+y-a \cos \left (b x \right ) = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11001

\[ {}y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right ) = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11002

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

11003

\[ {}y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11004

\[ {}y^{\prime \prime }+a^{2} y-\cot \left (a x \right ) = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11005

\[ {}y^{\prime \prime }+l y = 0 \]

[[_2nd_order, _missing_x]]

11007

\[ {}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11009

\[ {}y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11026

\[ {}y^{\prime \prime }+a y^{\prime }+b y = 0 \]

[[_2nd_order, _missing_x]]

11027

\[ {}y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right ) = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11030

\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11031

\[ {}y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11034

\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[_Hermite]

11036

\[ {}y^{\prime \prime }-x y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11038

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11040

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11041

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11042

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11047

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11048

\[ {}y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11049

\[ {}y^{\prime \prime }-x^{2} \left (x +1\right ) y^{\prime }+x \left (x^{4}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11050

\[ {}y^{\prime \prime }+x^{4} y^{\prime }-x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11052

\[ {}y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11053

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11055

\[ {}y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11062

\[ {}y^{\prime \prime }+2 a y^{\prime } \cot \left (a x \right )+\left (-a^{2}+b^{2}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11063

\[ {}y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (\frac {f \left (x \right )^{2}}{4}+\frac {f^{\prime }\left (x \right )}{2}+a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11073

\[ {}x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11075

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11080

\[ {}x y^{\prime \prime }-y^{\prime }-y a \,x^{3} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11082

\[ {}x y^{\prime \prime }+2 y^{\prime }-x y-{\mathrm e}^{x} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11083

\[ {}x y^{\prime \prime }+2 y^{\prime }+y a x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11091

\[ {}x y^{\prime \prime }-x y^{\prime }-y-x \left (x +1\right ) {\mathrm e}^{x} = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11093

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

11094

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-2 \left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11101

\[ {}x y^{\prime \prime }-2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x +2 a b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11103

\[ {}x y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11104

\[ {}x y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }-x \left (x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11105

\[ {}x y^{\prime \prime }-\left (2 a \,x^{2}+1\right ) y^{\prime }+b \,x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11107

\[ {}x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11108

\[ {}x y^{\prime \prime }+\left (2 a \,x^{3}-1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11109

\[ {}x y^{\prime \prime }+\left (2 a x \ln \left (x \right )+1\right ) y^{\prime }+\left (a^{2} x \ln \left (x \right )^{2}+a \ln \left (x \right )+a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11111

\[ {}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11112

\[ {}2 x y^{\prime \prime }+y^{\prime }+a y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11115

\[ {}\left (2 x -1\right ) y^{\prime \prime }-\left (-4+3 x \right ) y^{\prime }+\left (x -3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11117

\[ {}4 x y^{\prime \prime }+2 y^{\prime }-y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11118

\[ {}4 x y^{\prime \prime }+4 y^{\prime }-\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11128

\[ {}x^{2} y^{\prime \prime }-6 y = 0 \]

[[_Emden, _Fowler]]

11129

\[ {}x^{2} y^{\prime \prime }-12 y = 0 \]

[[_Emden, _Fowler]]

11130

\[ {}x^{2} y^{\prime \prime }+a y = 0 \]

[[_Emden, _Fowler]]

11132

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11133

\[ {}x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11134

\[ {}x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11140

\[ {}x^{2} y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+a b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11141

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y-a \,x^{2} = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11142

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+a y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11148

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y-3 x^{3} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11150

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11156

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11157

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right ) = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11158

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11159

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11160

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11161

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (a^{2} x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11163

\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11164

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11165

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-x^{2} \ln \left (x \right ) = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11166

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11168

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11169

\[ {}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0 \]

[[_Emden, _Fowler]]

11173

\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11174

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11175

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (x -9\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11176

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11178

\[ {}x^{2} y^{\prime \prime }-x \left (-1+x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11180

\[ {}x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11181

\[ {}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11183

\[ {}x^{2} y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11184

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11185

\[ {}x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11186

\[ {}x^{2} y^{\prime \prime }+\left (a +2 b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) b \,x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11190

\[ {}x^{2} y^{\prime \prime }+x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11191

\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11193

\[ {}x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (4 x^{4}+2 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11203

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11204

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11205

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11206

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11208

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11209

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+a y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11210

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11214

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2 = 0 \]

[[_2nd_order, _missing_y]]

11215

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+a y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11217

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11218

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0 \]

[[_2nd_order, _missing_y]]

11222

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-\left (3 x +1\right ) y^{\prime }-\left (x^{2}-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11223

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11227

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 a x y^{\prime }+a \left (a -1\right ) y = 0 \]

[_Gegenbauer]

11230

\[ {}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11231

\[ {}x \left (x +1\right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11233

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11234

\[ {}\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11242

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x^{2}+x -1\right ) y^{\prime }-\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11243

\[ {}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}} = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11244

\[ {}\left (x^{2}+3 x +4\right ) y^{\prime \prime }+\left (x^{2}+x +1\right ) y^{\prime }-\left (2 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11246

\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11247

\[ {}2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11250

\[ {}\left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11251

\[ {}4 x^{2} y^{\prime \prime }+y = 0 \]

[[_Emden, _Fowler]]

11256

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11257

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (a \,x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11259

\[ {}4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11260

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (4 x^{2}+12 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11261

\[ {}4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11262

\[ {}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11263

\[ {}4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (x^{2} \ln \left (x \right )^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

11264

\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11266

\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

11267

\[ {}9 x \left (-1+x \right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y = 0 \]

[_Jacobi]

11268

\[ {}16 x^{2} y^{\prime \prime }+\left (3+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11269

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }-\left (4 x +5\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11270

\[ {}\left (27 x^{2}+4\right ) y^{\prime \prime }+27 x y^{\prime }-3 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11272

\[ {}50 x \left (-1+x \right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y = 0 \]

[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11277

\[ {}\left (a \,x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+b y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11278

\[ {}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11279

\[ {}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y = 0 \]

[_Gegenbauer]

11280

\[ {}\left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11283

\[ {}x^{3} y^{\prime \prime }+x y^{\prime }-\left (2 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11286

\[ {}x^{3} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11287

\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11289

\[ {}x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+x y-1 = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11291

\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11294

\[ {}x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3} = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11298

\[ {}x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

11299

\[ {}x \left (x^{2}-2\right ) y^{\prime \prime }-\left (x^{3}+3 x^{2}-2 x -2\right ) y^{\prime }+\left (x^{2}+4 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11300

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

11301

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

11302

\[ {}y^{\prime \prime } = -\frac {2 \left (-2+x \right ) y^{\prime }}{x \left (-1+x \right )}+\frac {2 \left (x +1\right ) y}{x^{2} \left (-1+x \right )} \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11303

\[ {}y^{\prime \prime } = \frac {\left (5 x -4\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (-1+x \right )} \]

[[_2nd_order, _with_linear_symmetries]]

11305

\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x +1}-\frac {y}{x \left (x +1\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11307

\[ {}y^{\prime \prime } = \frac {2 y}{x \left (-1+x \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11310

\[ {}y^{\prime \prime } = \frac {\left (x -4\right ) y^{\prime }}{2 x \left (-2+x \right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (-2+x \right )} \]

[[_2nd_order, _with_linear_symmetries]]

11311

\[ {}y^{\prime \prime } = \frac {y^{\prime }}{x +1}-\frac {\left (3 x +1\right ) y}{4 x^{2} \left (x +1\right )} \]

[[_2nd_order, _with_linear_symmetries]]

11315

\[ {}y^{\prime \prime } = -\frac {\left (1-3 x \right ) y}{\left (-1+x \right ) \left (2 x -1\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11316

\[ {}y^{\prime \prime } = -\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (x +a \right ) \left (x +b \right )}-\frac {\left (a -b \right ) y}{4 \left (x +a \right )^{2} \left (x +b \right )} \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11317

\[ {}y^{\prime \prime } = \frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (-2+x \right )}+\frac {y}{3 x^{2} \left (-2+x \right )} \]

[[_2nd_order, _with_linear_symmetries]]

11319

\[ {}y^{\prime \prime } = \frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11321

\[ {}y^{\prime \prime } = -\frac {a y}{x^{4}} \]

[[_Emden, _Fowler]]

11324

\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x^{3}}+\frac {2 y}{x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

11325

\[ {}y^{\prime \prime } = \frac {\left (a +b \right ) y^{\prime }}{x^{2}}-\frac {\left (\left (a +b \right ) x +a b \right ) y}{x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

11329

\[ {}y^{\prime \prime } = -\frac {2 y^{\prime }}{x}-\frac {a^{2} y}{x^{4}} \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11330

\[ {}y^{\prime \prime } = -\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}+\frac {y}{x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

11331

\[ {}y^{\prime \prime } = -\frac {2 \left (x +a \right ) y^{\prime }}{x^{2}}-\frac {b y}{x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

11332

\[ {}y^{\prime \prime } = \frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

11333

\[ {}y^{\prime \prime } = \frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {2 y}{x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

11334

\[ {}y^{\prime \prime } = -\frac {\left (x^{3}-1\right ) y^{\prime }}{x \left (x^{3}+1\right )}+\frac {x y}{x^{3}+1} \]

[[_2nd_order, _with_linear_symmetries]]

11337

\[ {}y^{\prime \prime } = \frac {\left (x^{2}-2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (x^{2}-2\right ) y}{x^{2} \left (x^{2}-1\right )} \]

[[_2nd_order, _with_linear_symmetries]]

11340

\[ {}y^{\prime \prime } = \frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (a +1\right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \]

[[_2nd_order, _with_linear_symmetries]]

11344

\[ {}y^{\prime \prime } = -\frac {a y}{\left (x^{2}+1\right )^{2}} \]

[_Halm]

11345

\[ {}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11348

\[ {}y^{\prime \prime } = -\frac {a y}{\left (x^{2}-1\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11349

\[ {}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}-1}+\frac {a^{2} y}{\left (x^{2}-1\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11355

\[ {}y^{\prime \prime } = -\frac {\left (2 x^{2}+a \right ) y^{\prime }}{x \left (x^{2}+a \right )}-\frac {b y}{x^{2} \left (x^{2}+a \right )} \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

11356

\[ {}y^{\prime \prime } = -\frac {b^{2} y}{\left (a^{2}+x^{2}\right )^{2}} \]

[[_Emden, _Fowler]]

11357

\[ {}y^{\prime \prime } = -\frac {2 \left (x^{2}-1\right ) y^{\prime }}{x \left (-1+x \right )^{2}}-\frac {\left (-2 x^{2}+2 x +2\right ) y}{x^{2} \left (-1+x \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11358

\[ {}y^{\prime \prime } = \frac {12 y}{\left (x +1\right )^{2} \left (x^{2}+2 x +3\right )} \]

[[_2nd_order, _with_linear_symmetries]]

11359

\[ {}y^{\prime \prime } = -\frac {b y}{x^{2} \left (x -a \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11360

\[ {}y^{\prime \prime } = -\frac {b y}{x^{2} \left (x -a \right )^{2}}+c \]

[[_2nd_order, _linear, _nonhomogeneous]]

11361

\[ {}y^{\prime \prime } = \frac {c y}{\left (x -a \right )^{2} \left (x -b \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11362

\[ {}y^{\prime \prime } = -\frac {\left (\left (\alpha +\beta +1\right ) \left (x -a \right )^{2} \left (x -b \right )+\left (1-\alpha -\beta \right ) \left (x -b \right )^{2} \left (x -a \right )\right ) y^{\prime }}{\left (x -a \right )^{2} \left (x -b \right )^{2}}-\frac {\alpha \beta \left (a -b \right )^{2} y}{\left (x -a \right )^{2} \left (x -b \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11364

\[ {}y^{\prime \prime } = -\frac {\left (a \,x^{2}+a -3\right ) y}{4 \left (x^{2}+1\right )^{2}} \]

[_Halm]

11365

\[ {}y^{\prime \prime } = \frac {18 y}{\left (2 x +1\right )^{2} \left (x^{2}+x +1\right )} \]

[[_2nd_order, _with_linear_symmetries]]

11366

\[ {}y^{\prime \prime } = \frac {3 y}{4 \left (x^{2}+x +1\right )^{2}} \]

[[_Emden, _Fowler]]

11369

\[ {}y^{\prime \prime } = -\frac {3 y}{16 x^{2} \left (-1+x \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11373

\[ {}y^{\prime \prime } = -\frac {2 y^{\prime }}{x}-\frac {c y}{x^{2} \left (a x +b \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11374

\[ {}y^{\prime \prime } = -\frac {y}{\left (a x +b \right )^{4}} \]

[[_Emden, _Fowler]]

11375

\[ {}y^{\prime \prime } = -\frac {A y}{\left (a \,x^{2}+b x +c \right )^{2}} \]

[[_Emden, _Fowler]]

11376

\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x^{4}}+\frac {y}{x^{5}} \]

[[_2nd_order, _with_linear_symmetries]]

11378

\[ {}y^{\prime \prime } = \frac {\left (3 x +1\right ) y^{\prime }}{\left (-1+x \right ) \left (x +1\right )}-\frac {36 \left (x +1\right )^{2} y}{\left (-1+x \right )^{2} \left (3 x +5\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11383

\[ {}y^{\prime \prime } = -\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (-2 x^{2}+1\right ) y}{4 x^{6}} \]

[[_2nd_order, _with_linear_symmetries]]

11384

\[ {}y^{\prime \prime } = \frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (a \,x^{4}+10 x^{2}+1\right ) y}{4 x^{6}} \]

[[_2nd_order, _with_linear_symmetries]]

11385

\[ {}y^{\prime \prime } = -\frac {27 x y}{16 \left (x^{3}-1\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11400

\[ {}y^{\prime \prime } = -\frac {a \left (n -1\right ) \sin \left (2 a x \right ) y^{\prime }}{\cos \left (a x \right )^{2}}-\frac {n \,a^{2} \left (\left (n -1\right ) \sin \left (a x \right )^{2}+\cos \left (a x \right )^{2}\right ) y}{\cos \left (a x \right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

11421

\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-1+x \right ) y}{x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

11422

\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}} \]

[[_2nd_order, _with_linear_symmetries]]

11423

\[ {}y^{\prime \prime } = -\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

12422

\[ {}y^{\prime \prime }+a y = 0 \]

[[_2nd_order, _missing_x]]

12424

\[ {}y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12426

\[ {}y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12432

\[ {}y^{\prime \prime }+a y^{\prime }+b y = 0 \]

[[_2nd_order, _missing_x]]

12435

\[ {}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12436

\[ {}y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12445

\[ {}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12446

\[ {}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12447

\[ {}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12448

\[ {}y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12451

\[ {}y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12454

\[ {}y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12455

\[ {}y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12456

\[ {}y^{\prime \prime }+\left (a \,x^{2}+2 b \right ) y^{\prime }+\left (a b \,x^{2}-a x +b^{2}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12457

\[ {}y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12459

\[ {}y^{\prime \prime }+\left (a b \,x^{2}+b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12460

\[ {}y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+x \left (a b \,x^{2}+c b +2 a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12461

\[ {}y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a b \,x^{3}+a c \,x^{2}+b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12462

\[ {}y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a b \,x^{3}-a \,x^{2}+b^{2}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12463

\[ {}y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12464

\[ {}y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12482

\[ {}x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12490

\[ {}x y^{\prime \prime }+a x y^{\prime }+a y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12493

\[ {}x y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12496

\[ {}x y^{\prime \prime }-\left (a x +1\right ) y^{\prime }-b \,x^{2} \left (b x +a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12497

\[ {}x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12501

\[ {}x y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-\left (a c \,x^{2}+\left (c b +c^{2}+a \right ) x +b +2 c \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12502

\[ {}x y^{\prime \prime }+\left (a \,x^{2}+b x +2\right ) y^{\prime }+b y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12508

\[ {}x y^{\prime \prime }+x \left (a \,x^{2}+b \right ) y^{\prime }+\left (3 a \,x^{2}+b \right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12509

\[ {}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+2\right ) y^{\prime }+b x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12510

\[ {}x y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+a x -1\right ) y^{\prime }+a^{2} b \,x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12531

\[ {}x^{2} y^{\prime \prime }+a y = 0 \]

[[_Emden, _Fowler]]

12537

\[ {}x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12544

\[ {}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0 \]

[[_Emden, _Fowler]]

12549

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-\left (a^{2} x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12550

\[ {}x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (b^{2} x^{2}+a \left (a +1\right )\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12551

\[ {}x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (a +1\right )\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12561

\[ {}x^{2} y^{\prime \prime }+\left (a \,x^{2}+\left (a b -1\right ) x +b \right ) y^{\prime }+a^{2} b x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12572

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+a y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12573

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+n^{2} y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12576

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-3 x y^{\prime }+n \left (2+n \right ) y = 0 \]

[_Gegenbauer]

12583

\[ {}\left (a \,x^{2}+b \right ) y^{\prime \prime }+a x y^{\prime }+c y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12585

\[ {}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12586

\[ {}\left (a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12595

\[ {}\left (2 a x +x^{2}+b \right ) y^{\prime \prime }+\left (x +a \right ) y^{\prime }-m^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12598

\[ {}\left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+d y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12599

\[ {}\left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+3 \left (a x +b \right ) y^{\prime }+d y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12610

\[ {}x \left (a \,x^{2}+b \right ) y^{\prime \prime }+2 \left (a \,x^{2}+b \right ) y^{\prime }-2 y a x = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12613

\[ {}x^{2} \left (a x +b \right ) y^{\prime \prime }-2 x \left (a x +2 b \right ) y^{\prime }+2 \left (a x +3 b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12614

\[ {}x^{2} \left (a x +b \right ) y^{\prime \prime }+\left (a \left (2-n -m \right ) x^{2}-b \left (m +n \right ) x \right ) y^{\prime }+\left (a m \left (n -1\right ) x +b n \left (m +1\right )\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12632

\[ {}x^{4} y^{\prime \prime }+a y = 0 \]

[[_Emden, _Fowler]]

12634

\[ {}x^{4} y^{\prime \prime }-\left (a +b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) x +a b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12635

\[ {}x^{4} y^{\prime \prime }+2 x^{2} \left (x +a \right ) y^{\prime }+b y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12637

\[ {}x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12638

\[ {}x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y = c \,x^{2} \left (x -a \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12641

\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+a y = 0 \]

[_Halm]

12642

\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime }+a y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12643

\[ {}\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y = 0 \]

[[_Emden, _Fowler]]

12644

\[ {}\left (-a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12645

\[ {}4 \left (x^{2}+1\right )^{2} y^{\prime \prime }+\left (a \,x^{2}+a -3\right ) y = 0 \]

[_Halm]

12646

\[ {}\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+2 a x \left (a \,x^{2}+b \right ) y^{\prime }+c y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12650

\[ {}\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (2 a x +c \right ) \left (a \,x^{2}+b \right ) y^{\prime }+k y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12654

\[ {}\left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }-c y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12655

\[ {}\left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }+\left (x -a \right ) \left (x -b \right ) \left (2 x +\lambda \right ) y^{\prime }+\mu y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12656

\[ {}\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+A y = 0 \]

[[_Emden, _Fowler]]

12659

\[ {}\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+\left (2 a x +k \right ) \left (a \,x^{2}+b x +c \right ) y^{\prime }+m y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12698

\[ {}y^{\prime \prime }+2 a \,{\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{\lambda x}+\lambda \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12840

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

12841

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

12851

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12853

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12854

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

12856

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

12858

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

12859

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

12860

\[ {}y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

12861

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12862

\[ {}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x \]

[[_2nd_order, _linear, _nonhomogeneous]]

12863

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

12867

\[ {}y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1 \]

[[_2nd_order, _missing_y]]

12871

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

12872

\[ {}\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y = x \]

[[_2nd_order, _with_linear_symmetries]]

12873

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12875

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12880

\[ {}y^{\prime \prime }+4 y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12881

\[ {}y^{\prime \prime }+4 y = \sec \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12883

\[ {}y^{\prime \prime }+y = x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

12886

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x \]

[[_2nd_order, _with_linear_symmetries]]

12887

\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = x^{2}-x -1 \]

[[_2nd_order, _with_linear_symmetries]]

12888

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12889

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

12890

\[ {}\sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 \sin \left (x \right ) y = {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12891

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12893

\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12895

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

12897

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12898

\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

12899

\[ {}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0 \]

[_Laguerre]

12900

\[ {}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12901

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12902

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12903

\[ {}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12904

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12905

\[ {}\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12906

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

12911

\[ {}y^{\prime \prime }+x y^{\prime } = x \]

[[_2nd_order, _missing_y]]

12912

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

12921

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

12922

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 \left (-1+x \right ) y^{\prime }+2 y = \cos \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

12925

\[ {}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

12934

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2 \]

[[_2nd_order, _missing_y]]

12937

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2+4 x \right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

12939

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0 \]

[[_2nd_order, _missing_y]]

12942

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0 \]

[[_2nd_order, _missing_y]]

12949

\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 0 \]

[[_2nd_order, _missing_x]]

12953

\[ {}t^{2} x^{\prime \prime }-6 x = 0 \]

[[_Emden, _Fowler]]

12954

\[ {}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0 \]

[[_2nd_order, _missing_x]]

12959

\[ {}x^{\prime \prime } = -3 \sqrt {t} \]
i.c.

[[_2nd_order, _quadrature]]

12964

\[ {}x^{\prime }+t x^{\prime \prime } = 1 \]
i.c.

[[_2nd_order, _missing_y]]

12993

\[ {}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2 \]

[[_2nd_order, _missing_y]]

13017

\[ {}x^{\prime \prime }+x^{\prime } = 3 t \]

[[_2nd_order, _missing_y]]

13033

\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13034

\[ {}x^{\prime \prime }-2 x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13035

\[ {}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13036

\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13037

\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13038

\[ {}x^{\prime \prime }-2 x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13039

\[ {}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13040

\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13041

\[ {}x^{\prime \prime }+x^{\prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13042

\[ {}x^{\prime \prime }-4 x^{\prime }+6 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13043

\[ {}x^{\prime \prime }+9 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13044

\[ {}x^{\prime \prime }-12 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13045

\[ {}2 x^{\prime \prime }+3 x^{\prime }+3 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13046

\[ {}\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13047

\[ {}x^{\prime \prime }+x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13048

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13049

\[ {}x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

13050

\[ {}x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13051

\[ {}x^{\prime \prime }+x^{\prime }+x = 12 \]

[[_2nd_order, _missing_x]]

13052

\[ {}x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13053

\[ {}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13054

\[ {}x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13055

\[ {}x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13056

\[ {}x^{\prime \prime }+x^{\prime }+x = \left (t +2\right ) \sin \left (\pi t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13057

\[ {}x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

13058

\[ {}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13059

\[ {}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13060

\[ {}x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13061

\[ {}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13062

\[ {}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t} \]

[[_2nd_order, _missing_y]]

13063

\[ {}x^{\prime \prime }+x = t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

13064

\[ {}x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

13065

\[ {}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

13066

\[ {}x^{\prime \prime }-4 x = \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13067

\[ {}x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13068

\[ {}x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13069

\[ {}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13070

\[ {}x^{\prime \prime }-2 x^{\prime } = 4 \]
i.c.

[[_2nd_order, _missing_x]]

13071

\[ {}x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13072

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13073

\[ {}x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13074

\[ {}x^{\prime \prime }+3025 x = \cos \left (45 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13075

\[ {}x^{\prime \prime } = -\frac {x}{t^{2}} \]

[[_Emden, _Fowler]]

13076

\[ {}x^{\prime \prime } = \frac {4 x}{t^{2}} \]

[[_Emden, _Fowler]]

13077

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13078

\[ {}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13079

\[ {}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0 \]

[[_Emden, _Fowler]]

13080

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13081

\[ {}t^{2} x^{\prime \prime }+t x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_y]]

13082

\[ {}t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0 \]
i.c.

[[_Emden, _Fowler]]

13083

\[ {}x^{\prime \prime }+t^{2} x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_y]]

13084

\[ {}x^{\prime \prime }+x = \tan \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13085

\[ {}x^{\prime \prime }-x = t \,{\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13086

\[ {}x^{\prime \prime }-x = \frac {1}{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13087

\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13088

\[ {}x^{\prime \prime }+x = \frac {1}{t +1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13089

\[ {}x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13090

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{t} = a \]

[[_2nd_order, _missing_y]]

13091

\[ {}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \]

[[_2nd_order, _with_linear_symmetries]]

13092

\[ {}x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13168

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]

[[_2nd_order, _missing_x]]

13169

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

13170

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13175

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

[[_2nd_order, _missing_x]]

13180

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13182

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13185

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13188

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13310

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13311

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13313

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

13314

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13315

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13316

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13317

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

13326

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

13327

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

13328

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

13329

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

13330

\[ {}4 y^{\prime \prime }-12 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

13331

\[ {}3 y^{\prime \prime }-14 y^{\prime }-5 y = 0 \]

[[_2nd_order, _missing_x]]

13334

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

13335

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

13336

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

13337

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

13338

\[ {}y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

13339

\[ {}4 y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

13352

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13353

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13354

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13355

\[ {}3 y^{\prime \prime }+4 y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13356

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13357

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13358

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13359

\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13360

\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13361

\[ {}y^{\prime \prime }+6 y^{\prime }+58 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13362

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13363

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13364

\[ {}9 y^{\prime \prime }+6 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13365

\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13372

\[ {}y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

13373

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13374

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13375

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13376

\[ {}y^{\prime \prime }+2 y^{\prime }+4 y = \cos \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13377

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

13378

\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13379

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 5 x \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13384

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \]

[[_2nd_order, _linear, _nonhomogeneous]]

13385

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13392

\[ {}y^{\prime \prime }+y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13393

\[ {}y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13396

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13397

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13398

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 9 x \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13399

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13400

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13401

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13402

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13403

\[ {}y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13404

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13405

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13406

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13407

\[ {}y^{\prime \prime }-y = 3 x^{2} {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13408

\[ {}y^{\prime \prime }+y = 3 x^{2}-4 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13409

\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13412

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13413

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13414

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13415

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13416

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13426

\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13427

\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13428

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13429

\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13430

\[ {}y^{\prime \prime }+4 y = \sec \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13431

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13432

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13433

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \tan \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13434

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13435

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13436

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13437

\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13438

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{x}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13439

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{2 x}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13440

\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13441

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \arcsin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13442

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13443

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \ln \left (x \right ) x \]

[[_2nd_order, _linear, _nonhomogeneous]]

13444

\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13445

\[ {}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

13446

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = \left (2+x \right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

13447

\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

13448

\[ {}x \left (-2+x \right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (-1+x \right ) y = 3 x^{2} \left (-2+x \right )^{2} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13449

\[ {}\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13452

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \]

[[_Emden, _Fowler]]

13453

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13454

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13455

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13456

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13457

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

[[_Emden, _Fowler]]

13458

\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13459

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13460

\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13461

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \]

[[_Emden, _Fowler]]

13465

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6 \]

[[_2nd_order, _with_linear_symmetries]]

13466

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

13467

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13468

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 \ln \left (x \right ) x \]

[[_2nd_order, _with_linear_symmetries]]

13469

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13471

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13472

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13473

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

13474

\[ {}x^{2} y^{\prime \prime }-2 y = 4 x -8 \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13475

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13476

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13477

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13478

\[ {}x^{2} y^{\prime \prime }-6 y = \ln \left (x \right ) \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13479

\[ {}\left (2+x \right )^{2} y^{\prime \prime }-\left (2+x \right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13480

\[ {}\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13583

\[ {}t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13585

\[ {}\left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13587

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x = 0 \]

[[_Emden, _Fowler]]

13589

\[ {}t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13590

\[ {}t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13593

\[ {}\frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13594

\[ {}t^{2} x^{\prime \prime }+t x^{\prime }+x = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13599

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13600

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13601

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13602

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13603

\[ {}y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13604

\[ {}y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13605

\[ {}2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13606

\[ {}-\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13671

\[ {}x^{\prime \prime }-3 x^{\prime }+2 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13672

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13673

\[ {}z^{\prime \prime }-4 z^{\prime }+13 z = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13674

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13675

\[ {}y^{\prime \prime }-4 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13676

\[ {}\theta ^{\prime \prime }+4 \theta = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13677

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13678

\[ {}2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13679

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13680

\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13681

\[ {}4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13682

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13683

\[ {}y^{\prime \prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13684

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13685

\[ {}y^{\prime \prime }+\omega ^{2} y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13686

\[ {}x^{\prime \prime }-4 x = t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

13687

\[ {}x^{\prime \prime }-4 x^{\prime } = t^{2} \]

[[_2nd_order, _missing_y]]

13688

\[ {}x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

13689

\[ {}x^{\prime \prime }+x^{\prime }-2 x = {\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

13690

\[ {}x^{\prime \prime }+2 x^{\prime }+x = {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

13691

\[ {}x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13692

\[ {}x^{\prime \prime }+\omega ^{2} x = \sin \left (\omega t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13693

\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

13694

\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13695

\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13696

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t} \]

[[_2nd_order, _with_linear_symmetries]]

13697

\[ {}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13698

\[ {}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13699

\[ {}x^{\prime \prime }+\omega ^{2} x = \cos \left (\alpha t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13700

\[ {}x^{\prime \prime }+\omega ^{2} x = \cos \left (\omega t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13711

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

13712

\[ {}x^{\prime \prime }-x = \frac {1}{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13713

\[ {}y^{\prime \prime }+4 y = \cot \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13714

\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13715

\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \]

[[_2nd_order, _missing_y]]

13717

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

13718

\[ {}4 x^{2} y^{\prime \prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

13719

\[ {}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \]
i.c.

[[_Emden, _Fowler]]

13720

\[ {}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

13721

\[ {}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0 \]
i.c.

[[_Emden, _Fowler]]

13722

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

13723

\[ {}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]
i.c.

[[_Emden, _Fowler]]

13724

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = 0 \]
i.c.

[[_Emden, _Fowler]]

13725

\[ {}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

13726

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \]
i.c.

[[_Emden, _Fowler]]

13727

\[ {}a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y = 0 \]

[[_2nd_order, _missing_x]]

13821

\[ {}y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]
i.c.

[[_2nd_order, _missing_x]]

13822

\[ {}x^{\prime \prime }+x = \sin \left (t \right )-\cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13824

\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13825

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2 \]

[[_2nd_order, _with_linear_symmetries]]

13826

\[ {}y^{\prime \prime }+y = \cosh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13828

\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

13839

\[ {}y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13840

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \]

[[_2nd_order, _missing_y]]

13843

\[ {}x^{\prime \prime }+9 x = t \sin \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13844

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13846

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = x \,{\mathrm e}^{x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13847

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

13852

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 2 \cos \left (\ln \left (x +1\right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13856

\[ {}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13862

\[ {}y^{\prime \prime }+y = \sin \left (3 x \right ) \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13893

\[ {}x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13894

\[ {}y^{\prime \prime } = x^{2}+y \]

[[_2nd_order, _with_linear_symmetries]]

13901

\[ {}y^{\prime \prime }+4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

13903

\[ {}2 y^{\prime \prime }-3 y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

13911

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13914

\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13916

\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13917

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13918

\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13920

\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13922

\[ {}x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

13925

\[ {}x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

13932

\[ {}y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13933

\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

[[_2nd_order, _with_linear_symmetries]]

13934

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (2+x \right ) y}{x^{2} \left (x +1\right )} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13935

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

13936

\[ {}\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (3 x +1\right ) y^{\prime }}{x}+\frac {y}{x} = 3 x \]

[[_2nd_order, _linear, _nonhomogeneous]]

13939

\[ {}y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

14008

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

14013

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 1 \]

[[_2nd_order, _missing_x]]

14014

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

14015

\[ {}y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]

[[_2nd_order, _missing_x]]

14017

\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

14053

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{{3}/{2}} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

14054

\[ {}y^{\prime \prime }+4 y = 2 \sec \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14055

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x \]

[[_2nd_order, _linear, _nonhomogeneous]]

14056

\[ {}y^{\prime \prime }+y = f \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14057

\[ {}x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

14058

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

14070

\[ {}y^{\prime \prime }+\alpha ^{2} y = 0 \]

[[_2nd_order, _missing_x]]

14071

\[ {}y^{\prime \prime }-\alpha ^{2} y = 0 \]

[[_2nd_order, _missing_x]]

14072

\[ {}y^{\prime \prime }+\beta y^{\prime }+\gamma y = 0 \]

[[_2nd_order, _missing_x]]

14080

\[ {}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

14081

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

14082

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0 \]

[[_2nd_order, _missing_y]]

14149

\[ {}y^{\prime \prime } = a^{2} y \]

[[_2nd_order, _missing_x]]

14151

\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _missing_y]]

14158

\[ {}y^{\prime \prime } = 9 y \]

[[_2nd_order, _missing_x]]

14159

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

14160

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

14161

\[ {}y^{\prime \prime }+12 y = 7 y^{\prime } \]

[[_2nd_order, _missing_x]]

14162

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

14163

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

14164

\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

14165

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

14166

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

14175

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = x \]

[[_2nd_order, _with_linear_symmetries]]

14176

\[ {}s^{\prime \prime }-a^{2} s = t +1 \]

[[_2nd_order, _with_linear_symmetries]]

14177

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14178

\[ {}y^{\prime \prime }-y = 5 x +2 \]

[[_2nd_order, _with_linear_symmetries]]

14179

\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

14180

\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

14181

\[ {}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

14182

\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \]

[[_2nd_order, _missing_y]]

14183

\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = {\mathrm e}^{-x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14184

\[ {}y^{\prime \prime }+4 y = 2 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14188

\[ {}y^{\prime \prime }+2 h y^{\prime }+n^{2} y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14189

\[ {}y^{\prime \prime }+n^{2} y = h \sin \left (r x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14190

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14191

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14192

\[ {}y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

14199

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14202

\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14231

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

14233

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

14234

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

14235

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

14241

\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_Emden, _Fowler]]

14244

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

[[_2nd_order, _missing_x]]

14245

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

14248

\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

14249

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

14250

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

14256

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

14258

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

14261

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14262

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14263

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14264

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14266

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

14267

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

14268

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

14269

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

14270

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

14401

\[ {}3 y^{\prime \prime }-2 y^{\prime }+4 y = x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14403

\[ {}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \]
i.c.

[[_2nd_order, _missing_y]]

14404

\[ {}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \]
i.c.

[[_2nd_order, _missing_y]]

14407

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

14408

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

14409

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_Emden, _Fowler]]

14411

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14413

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

14414

\[ {}y^{\prime \prime }-4 y = 31 \]
i.c.

[[_2nd_order, _missing_x]]

14415

\[ {}y^{\prime \prime }+9 y = 27 x +18 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14416

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -3 x -\frac {3}{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14417

\[ {}4 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

14427

\[ {}y^{\prime \prime }+\alpha y = 0 \]

[[_2nd_order, _missing_x]]

14783

\[ {}y^{\prime \prime }-6 y^{\prime }-7 y = 0 \]

[[_2nd_order, _missing_x]]

14784

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]

[[_2nd_order, _missing_x]]

14814

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14815

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14816

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14817

\[ {}y^{\prime \prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14818

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \]

[[_2nd_order, _with_linear_symmetries]]

14819

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \]

[[_2nd_order, _with_linear_symmetries]]

14820

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t} \]

[[_2nd_order, _with_linear_symmetries]]

14821

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

14822

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

14823

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

14824

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t} \]

[[_2nd_order, _with_linear_symmetries]]

14825

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t} \]

[[_2nd_order, _with_linear_symmetries]]

14826

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14827

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14828

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14829

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14830

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14831

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14832

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14833

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14834

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14835

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14836

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

14837

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 5 \]
i.c.

[[_2nd_order, _missing_x]]

14838

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 2 \]
i.c.

[[_2nd_order, _missing_x]]

14839

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 10 \]
i.c.

[[_2nd_order, _missing_x]]

14840

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \]
i.c.

[[_2nd_order, _missing_x]]

14841

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14842

\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14843

\[ {}y^{\prime \prime }+2 y = -3 \]
i.c.

[[_2nd_order, _missing_x]]

14844

\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14845

\[ {}y^{\prime \prime }+9 y = 6 \]
i.c.

[[_2nd_order, _missing_x]]

14846

\[ {}y^{\prime \prime }+2 y = -{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14847

\[ {}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14848

\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \]
i.c.

[[_2nd_order, _missing_y]]

14849

\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \]
i.c.

[[_2nd_order, _missing_y]]

14850

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14851

\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14852

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14853

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14854

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14855

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14856

\[ {}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14857

\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14858

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14859

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14860

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14861

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14862

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14863

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14864

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14865

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14866

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14867

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14868

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14869

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14870

\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14871

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14872

\[ {}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14873

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14874

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14875

\[ {}y^{\prime \prime }+9 y = \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14876

\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14877

\[ {}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14878

\[ {}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14879

\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14905

\[ {}y^{\prime \prime } = \frac {x +1}{-1+x} \]

[[_2nd_order, _quadrature]]

14906

\[ {}x^{2} y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

14908

\[ {}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

14909

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

14919

\[ {}y^{\prime \prime } = \sin \left (2 x \right ) \]

[[_2nd_order, _quadrature]]

14920

\[ {}y^{\prime \prime }-3 = x \]

[[_2nd_order, _quadrature]]

14928

\[ {}x y^{\prime \prime }+2 = \sqrt {x} \]
i.c.

[[_2nd_order, _quadrature]]

15130

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

[[_2nd_order, _missing_y]]

15131

\[ {}x y^{\prime \prime } = 2 y^{\prime } \]

[[_2nd_order, _missing_y]]

15132

\[ {}y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

15133

\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _missing_y]]

15134

\[ {}x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime } \]

[[_2nd_order, _missing_y]]

15135

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

15142

\[ {}y^{\prime \prime } = 2 y^{\prime }-6 \]

[[_2nd_order, _missing_x]]

15144

\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _missing_y]]

15152

\[ {}y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

15158

\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \]

[[_2nd_order, _missing_y]]

15162

\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _missing_y]]

15164

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]
i.c.

[[_2nd_order, _missing_y]]

15165

\[ {}x y^{\prime \prime } = 2 y^{\prime } \]
i.c.

[[_2nd_order, _missing_y]]

15166

\[ {}y^{\prime \prime } = y^{\prime } \]
i.c.

[[_2nd_order, _missing_x]]

15167

\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _missing_y]]

15170

\[ {}x y^{\prime \prime }+2 y^{\prime } = 6 \]
i.c.

[[_2nd_order, _missing_y]]

15190

\[ {}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15217

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15218

\[ {}y^{\prime \prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15219

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15220

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15221

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15222

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15223

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

15224

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15225

\[ {}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15226

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15227

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15230

\[ {}y^{\prime \prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15231

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15232

\[ {}y^{\prime \prime }-10 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15233

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15236

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

15237

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 0 \]

[[_2nd_order, _missing_x]]

15238

\[ {}y^{\prime \prime }-25 y = 0 \]

[[_2nd_order, _missing_x]]

15239

\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

15240

\[ {}4 y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

15241

\[ {}3 y^{\prime \prime }+7 y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

15242

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15243

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15244

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15245

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15246

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15247

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15248

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

15249

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

15250

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

15251

\[ {}25 y^{\prime \prime }-10 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

15252

\[ {}16 y^{\prime \prime }-24 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

15253

\[ {}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

15254

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15255

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15256

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15257

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15258

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15259

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15260

\[ {}y^{\prime \prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

15261

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

15262

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

15263

\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \]

[[_2nd_order, _missing_x]]

15264

\[ {}9 y^{\prime \prime }+18 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

15265

\[ {}4 y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

15266

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15267

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15268

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15269

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15270

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15271

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15272

\[ {}y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15273

\[ {}y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15300

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15301

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

15302

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

15303

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15304

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

15305

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler]]

15306

\[ {}4 x^{2} y^{\prime \prime }+y = 0 \]

[[_Emden, _Fowler]]

15307

\[ {}x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y = 0 \]

[[_Emden, _Fowler]]

15308

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+29 y = 0 \]

[[_Emden, _Fowler]]

15309

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+10 y = 0 \]

[[_Emden, _Fowler]]

15310

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y = 0 \]

[[_Emden, _Fowler]]

15311

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15312

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

15313

\[ {}4 x^{2} y^{\prime \prime }+37 y = 0 \]

[[_Emden, _Fowler]]

15314

\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

15315

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-25 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15316

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

15317

\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 0 \]

[[_Emden, _Fowler]]

15318

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15319

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15320

\[ {}x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y = 0 \]
i.c.

[[_Emden, _Fowler]]

15321

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

15322

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler]]

15323

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]
i.c.

[[_Emden, _Fowler]]

15332

\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15333

\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15334

\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15335

\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15336

\[ {}y^{\prime \prime }-9 y = 36 \]
i.c.

[[_2nd_order, _missing_x]]

15337

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -6 \,{\mathrm e}^{4 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15338

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{5 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15339

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 169 \sin \left (2 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15340

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 10 x +12 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15342

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

15343

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

15344

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15345

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15346

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

15347

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x \]

[[_2nd_order, _with_linear_symmetries]]

15348

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 22 x +24 \]

[[_2nd_order, _with_linear_symmetries]]

15349

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

15350

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x \]

[[_2nd_order, _with_linear_symmetries]]

15351

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

15352

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 4 x^{2}+2 x +3 \]

[[_2nd_order, _with_linear_symmetries]]

15353

\[ {}y^{\prime \prime }+9 y = 52 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

15354

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x} \]

[[_2nd_order, _with_linear_symmetries]]

15355

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x} \]

[[_2nd_order, _with_linear_symmetries]]

15356

\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}} \]

[[_2nd_order, _missing_y]]

15357

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15358

\[ {}y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15359

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15360

\[ {}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \]

[[_2nd_order, _missing_y]]

15361

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15362

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15363

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -200 \]

[[_2nd_order, _missing_x]]

15364

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15365

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4 \]

[[_2nd_order, _with_linear_symmetries]]

15366

\[ {}y^{\prime \prime }+9 y = 9 x^{4}-9 \]

[[_2nd_order, _linear, _nonhomogeneous]]

15367

\[ {}y^{\prime \prime }+9 y = x^{3} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15368

\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15369

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15370

\[ {}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15371

\[ {}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

15372

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15373

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15374

\[ {}y^{\prime \prime }+9 y = 39 x \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15375

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

15376

\[ {}y^{\prime \prime }+4 y^{\prime } = 20 \]

[[_2nd_order, _missing_x]]

15377

\[ {}y^{\prime \prime }+4 y^{\prime } = x^{2} \]

[[_2nd_order, _missing_y]]

15378

\[ {}y^{\prime \prime }+9 y = 3 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15379

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15380

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15381

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15382

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

15383

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x} \]

[[_2nd_order, _with_linear_symmetries]]

15384

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15385

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15386

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15387

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15388

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 100 \]

[[_2nd_order, _missing_x]]

15389

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

15390

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8 \]

[[_2nd_order, _with_linear_symmetries]]

15391

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15392

\[ {}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15393

\[ {}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15394

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15395

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15396

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15397

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

15398

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x} \]

[[_2nd_order, _with_linear_symmetries]]

15399

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15400

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15401

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15402

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15403

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15404

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15405

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15406

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15407

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15422

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15423

\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15424

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15425

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15426

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \]

[[_2nd_order, _with_linear_symmetries]]

15427

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \]

[[_2nd_order, _with_linear_symmetries]]

15428

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15429

\[ {}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15430

\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

15431

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15432

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

15433

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 x^{2} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15434

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 \sqrt {x} \]

[[_2nd_order, _with_linear_symmetries]]

15435

\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15436

\[ {}y^{\prime \prime }+4 y = \csc \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15437

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15438

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15439

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15440

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15441

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

15442

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

15443

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

15444

\[ {}x^{2} y^{\prime \prime }-2 y = \frac {1}{-2+x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15445

\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15446

\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15447

\[ {}\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y = \left (x +1\right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

15448

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15449

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15456

\[ {}y^{\prime \prime }+36 y = 0 \]

[[_2nd_order, _missing_x]]

15457

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

[[_2nd_order, _missing_x]]

15458

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15459

\[ {}y^{\prime \prime }-36 y = 0 \]

[[_2nd_order, _missing_x]]

15460

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 0 \]

[[_2nd_order, _missing_x]]

15461

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

[[_Emden, _Fowler]]

15462

\[ {}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x} \]

[[_2nd_order, _missing_y]]

15464

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

15465

\[ {}y^{\prime \prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

15466

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

15467

\[ {}x^{2} y^{\prime \prime }+\frac {5 y}{2} = 0 \]

[[_Emden, _Fowler]]

15469

\[ {}x^{2} y^{\prime \prime }-6 y = 0 \]

[[_Emden, _Fowler]]

15470

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

15472

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15473

\[ {}y^{\prime \prime }-8 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

15474

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y = 0 \]

[[_Emden, _Fowler]]

15475

\[ {}y^{\prime \prime }+y^{\prime }-30 y = 0 \]

[[_2nd_order, _missing_x]]

15476

\[ {}16 y^{\prime \prime }-8 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

15477

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

15479

\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15480

\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15482

\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 = 0 \]

[[_2nd_order, _missing_x]]

15483

\[ {}y^{\prime \prime }+20 y^{\prime }+100 y = 0 \]

[[_2nd_order, _missing_x]]

15484

\[ {}x y^{\prime \prime } = 3 y^{\prime } \]

[[_2nd_order, _missing_y]]

15485

\[ {}y^{\prime \prime }-5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

15486

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

15487

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15488

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15489

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15490

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x} \]

[[_2nd_order, _with_linear_symmetries]]

15491

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15492

\[ {}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15493

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

15494

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15495

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

15496

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15498

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6 \]

[[_2nd_order, _with_linear_symmetries]]

15499

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15500

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15501

\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15504

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (x +1\right )^{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15505

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

15702

\[ {}y^{\prime \prime }+y^{\prime }-2 y = x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15706

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

15714

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]

[[_2nd_order, _missing_x]]

15715

\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

15716

\[ {}x^{\prime \prime }+2 x^{\prime }-10 x = 0 \]

[[_2nd_order, _missing_x]]

15717

\[ {}x^{\prime \prime }+x = t \cos \left (t \right )-\cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15718

\[ {}y^{\prime \prime }-12 y^{\prime }+40 y = 0 \]

[[_2nd_order, _missing_x]]

15721

\[ {}x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0 \]

[[_Emden, _Fowler]]

15722

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

15743

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15744

\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15747

\[ {}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0 \]
i.c.

[[_Emden, _Fowler]]

15748

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0 \]
i.c.

[[_Emden, _Fowler]]

15756

\[ {}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0 \]

[[_2nd_order, _missing_x]]

15765

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 0 \]

[[_2nd_order, _missing_x]]

15766

\[ {}y^{\prime \prime }-6 y^{\prime }+45 y = 0 \]

[[_2nd_order, _missing_x]]

15767

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0 \]

[[_Emden, _Fowler]]

15768

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

15769

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = x \]

[[_2nd_order, _with_linear_symmetries]]

15770

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 2 \]

[[_2nd_order, _missing_x]]

15778

\[ {}y^{\prime \prime }+4 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15779

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]
i.c.

[[_Emden, _Fowler]]

15922

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16098

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

16099

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16100

\[ {}2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y = 0 \]

[[_Emden, _Fowler]]

16101

\[ {}y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

16102

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16103

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16104

\[ {}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0 \]
i.c.

[[_Emden, _Fowler]]

16105

\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0 \]
i.c.

[[_Emden, _Fowler]]

16106

\[ {}y^{\prime \prime }+y = 2 \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16107

\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 0 \]

[[_2nd_order, _missing_x]]

16108

\[ {}y^{\prime \prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

16109

\[ {}y^{\prime \prime }+6 y^{\prime }+18 y = 0 \]

[[_2nd_order, _missing_x]]

16110

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

16121

\[ {}a y^{\prime \prime }+b y^{\prime }+c y = 0 \]

[[_2nd_order, _missing_x]]

16122

\[ {}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0 \]

[[_Emden, _Fowler]]

16127

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

16128

\[ {}y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]

[[_2nd_order, _missing_x]]

16129

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

16130

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

16131

\[ {}y^{\prime \prime }+8 y^{\prime }+12 y = 0 \]

[[_2nd_order, _missing_x]]

16132

\[ {}y^{\prime \prime }+5 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16133

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16134

\[ {}4 y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

16135

\[ {}y^{\prime \prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

16136

\[ {}y^{\prime \prime }+8 y = 0 \]

[[_2nd_order, _missing_x]]

16137

\[ {}y^{\prime \prime }+7 y = 0 \]

[[_2nd_order, _missing_x]]

16138

\[ {}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

16139

\[ {}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

16140

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16141

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

16142

\[ {}y^{\prime \prime }-y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16143

\[ {}3 y^{\prime \prime }-y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16144

\[ {}y^{\prime \prime }+y^{\prime }-12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16145

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16146

\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16147

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16148

\[ {}y^{\prime \prime }+36 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16149

\[ {}y^{\prime \prime }+100 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16150

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16151

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16152

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16153

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16154

\[ {}y^{\prime \prime }+y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16155

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16156

\[ {}y^{\prime \prime }-y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16157

\[ {}y^{\prime \prime }-y^{\prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16158

\[ {}6 y^{\prime \prime }+5 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16159

\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16160

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 0 \]

[[_2nd_order, _missing_x]]

16161

\[ {}3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

16162

\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

16163

\[ {}a y^{\prime \prime }+2 b y^{\prime }+c y = 0 \]

[[_2nd_order, _missing_x]]

16164

\[ {}y^{\prime \prime }+6 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

16165

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

16166

\[ {}y^{\prime \prime }-6 y^{\prime }-16 y = 0 \]

[[_2nd_order, _missing_x]]

16167

\[ {}y^{\prime \prime }-16 y = 0 \]

[[_2nd_order, _missing_x]]

16168

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16171

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16172

\[ {}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t} \]

[[_2nd_order, _with_linear_symmetries]]

16173

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t} \]

[[_2nd_order, _with_linear_symmetries]]

16174

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t} \]

[[_2nd_order, _with_linear_symmetries]]

16175

\[ {}y^{\prime \prime }-y = 2 t -4 \]

[[_2nd_order, _with_linear_symmetries]]

16176

\[ {}y^{\prime \prime }-2 y^{\prime }+y = t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

16177

\[ {}y^{\prime \prime }+2 y^{\prime } = 3-4 t \]

[[_2nd_order, _missing_y]]

16178

\[ {}y^{\prime \prime }+y = \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16179

\[ {}y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16180

\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right )+t \]

[[_2nd_order, _linear, _nonhomogeneous]]

16181

\[ {}y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16182

\[ {}y^{\prime \prime } = 3 t^{4}-2 t \]

[[_2nd_order, _quadrature]]

16183

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16184

\[ {}y^{\prime \prime }+y^{\prime }-2 y = -1 \]

[[_2nd_order, _missing_x]]

16185

\[ {}5 y^{\prime \prime }+y^{\prime }-4 y = -3 \]

[[_2nd_order, _missing_x]]

16186

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t \]

[[_2nd_order, _with_linear_symmetries]]

16187

\[ {}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t \]

[[_2nd_order, _with_linear_symmetries]]

16188

\[ {}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t \]

[[_2nd_order, _with_linear_symmetries]]

16189

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

16190

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

16191

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16192

\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \]

[[_2nd_order, _missing_y]]

16193

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16194

\[ {}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16195

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16196

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16197

\[ {}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

16198

\[ {}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16199

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16200

\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

16201

\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \]

[[_2nd_order, _missing_y]]

16202

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

16203

\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \]

[[_2nd_order, _missing_y]]

16204

\[ {}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \]

[[_2nd_order, _quadrature]]

16205

\[ {}y^{\prime \prime }+3 y^{\prime } = 18 \]
i.c.

[[_2nd_order, _missing_x]]

16206

\[ {}y^{\prime \prime }-y = 4 \]
i.c.

[[_2nd_order, _missing_x]]

16207

\[ {}y^{\prime \prime }-4 y = 32 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16208

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = -2 \]
i.c.

[[_2nd_order, _missing_x]]

16209

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 3 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16210

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 4 \]
i.c.

[[_2nd_order, _missing_x]]

16211

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16212

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = -1 \]
i.c.

[[_2nd_order, _missing_x]]

16213

\[ {}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t \]
i.c.

[[_2nd_order, _missing_y]]

16214

\[ {}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _missing_y]]

16215

\[ {}y^{\prime \prime }-2 y^{\prime } = 2 t^{2} \]
i.c.

[[_2nd_order, _missing_y]]

16216

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _missing_y]]

16217

\[ {}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _missing_y]]

16218

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16220

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16226

\[ {}y^{\prime \prime }+y^{\prime }-2 y = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16227

\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16228

\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16229

\[ {}y^{\prime \prime }+4 y = 1 \]

[[_2nd_order, _missing_x]]

16230

\[ {}y^{\prime \prime }+16 y^{\prime } = t \]

[[_2nd_order, _missing_y]]

16231

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t} \]

[[_2nd_order, _with_linear_symmetries]]

16232

\[ {}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16233

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16234

\[ {}y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16235

\[ {}y^{\prime \prime }+16 y = \csc \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16236

\[ {}y^{\prime \prime }+16 y = \cot \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16237

\[ {}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16238

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16239

\[ {}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16240

\[ {}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16241

\[ {}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16242

\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16243

\[ {}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16244

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16245

\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16246

\[ {}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16247

\[ {}y^{\prime \prime }-y = 2 \sinh \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16248

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16249

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16250

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16251

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16252

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16253

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16254

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16255

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16256

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16257

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16258

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16259

\[ {}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16260

\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16261

\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16262

\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16263

\[ {}y^{\prime \prime }+4 y = \tan \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16264

\[ {}y^{\prime \prime }+16 y = \tan \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16265

\[ {}y^{\prime \prime }+4 y = \tan \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16266

\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \tan \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16267

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right ) \tan \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16268

\[ {}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16269

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )^{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16270

\[ {}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16271

\[ {}y^{\prime \prime }+y = \tan \left (t \right )^{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16272

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16273

\[ {}y^{\prime \prime }+9 y = \csc \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16274

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16275

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16276

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+4 y = t \]

[[_2nd_order, _with_linear_symmetries]]

16277

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16278

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16279

\[ {}y^{\prime \prime }+4 y = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16281

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16283

\[ {}t y^{\prime \prime }+2 y^{\prime }+t y = -t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16285

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16361

\[ {}4 x^{2} y^{\prime \prime }-8 x y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16362

\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16363

\[ {}2 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \]

[[_Emden, _Fowler]]

16364

\[ {}2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y = 0 \]

[[_Emden, _Fowler]]

16365

\[ {}4 x^{2} y^{\prime \prime }+17 y = 0 \]

[[_Emden, _Fowler]]

16366

\[ {}9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y = 0 \]

[[_Emden, _Fowler]]

16367

\[ {}2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y = 0 \]

[[_Emden, _Fowler]]

16368

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \]

[[_Emden, _Fowler]]

16369

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0 \]

[[_Emden, _Fowler]]

16370

\[ {}4 x^{2} y^{\prime \prime }+y = 0 \]

[[_Emden, _Fowler]]

16371

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

16372

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

16381

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \frac {1}{x^{5}} \]

[[_2nd_order, _with_linear_symmetries]]

16382

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

16383

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

16384

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \frac {1}{x^{2}} \]

[[_2nd_order, _with_linear_symmetries]]

16385

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2 x \]

[[_2nd_order, _with_linear_symmetries]]

16386

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

16387

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 8 \]

[[_2nd_order, _with_linear_symmetries]]

16388

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+36 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

16391

\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16392

\[ {}2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y = 0 \]
i.c.

[[_Emden, _Fowler]]

16393

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16394

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16399

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x^{2}} \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16400

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (x \right ) \]
i.c.

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

16401

\[ {}4 x^{2} y^{\prime \prime }+y = x^{3} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16402

\[ {}9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16403

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

16404

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

16405

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16410

\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16411

\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16412

\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16413

\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16414

\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16415

\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16416

\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16417

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

16418

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

16419

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16420

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

16427

\[ {}6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16479

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

16480

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

16481

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

16484

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

16485

\[ {}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

16486

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16487

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

16488

\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = 0 \]

[[_2nd_order, _missing_x]]

16489

\[ {}2 y^{\prime \prime }-5 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

16490

\[ {}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

16491

\[ {}20 y^{\prime \prime }+y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

16492

\[ {}12 y^{\prime \prime }+8 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16496

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = -t \]

[[_2nd_order, _with_linear_symmetries]]

16497

\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \]

[[_2nd_order, _missing_y]]

16498

\[ {}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right ) \]

[[_2nd_order, _missing_y]]

16499

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16500

\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16501

\[ {}y^{\prime \prime }-2 y^{\prime } = \frac {1}{1+{\mathrm e}^{2 t}} \]

[[_2nd_order, _missing_y]]

16502

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = -4 \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

16503

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

16504

\[ {}y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16505

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16510

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16511

\[ {}y^{\prime \prime }+10 y^{\prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16512

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16513

\[ {}y^{\prime \prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16514

\[ {}y^{\prime \prime }-4 y = t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16515

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16516

\[ {}y^{\prime \prime }+9 y = \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16517

\[ {}y^{\prime \prime }+y = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16518

\[ {}y^{\prime \prime }+4 y = \tan \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16519

\[ {}y^{\prime \prime }+y = \csc \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16520

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16521

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16522

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16523

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16524

\[ {}y^{\prime \prime }-2 t y^{\prime }+t^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

16525

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

16526

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

16527

\[ {}t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

16528

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \]

[[_Emden, _Fowler]]

16529

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16530

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

16531

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

16532

\[ {}5 x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

16533

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \]

[[_Emden, _Fowler]]

16534

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \]

[[_2nd_order, _with_linear_symmetries]]

16544

\[ {}4 x^{\prime \prime }+9 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16545

\[ {}9 x^{\prime \prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16546

\[ {}x^{\prime \prime }+64 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16547

\[ {}x^{\prime \prime }+100 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16548

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16549

\[ {}x^{\prime \prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16550

\[ {}x^{\prime \prime }+16 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16551

\[ {}x^{\prime \prime }+256 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16552

\[ {}x^{\prime \prime }+9 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16553

\[ {}10 x^{\prime \prime }+\frac {x}{10} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16554

\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16555

\[ {}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16556

\[ {}\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16557

\[ {}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16558

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16559

\[ {}x^{\prime \prime }+4 x^{\prime }+20 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16560

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16562

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16563

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ -t +1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16564

\[ {}x^{\prime \prime }+x = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16565

\[ {}x^{\prime \prime }+x = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16566

\[ {}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16567

\[ {}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16568

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16581

\[ {}x^{\prime \prime }-3 x^{\prime }+4 x = 0 \]

[[_2nd_order, _missing_x]]

16582

\[ {}x^{\prime \prime }+6 x^{\prime }+9 x = 0 \]

[[_2nd_order, _missing_x]]

16583

\[ {}x^{\prime \prime }+16 x = t \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16584

\[ {}x^{\prime \prime }+x = {\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

16827

\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right )+2 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16830

\[ {}\left (-1+x \right ) y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

16832

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16833

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \]

[[_2nd_order, _missing_x]]

16838

\[ {}y^{\prime \prime } \left (2+x \right )^{5} = 1 \]
i.c.

[[_2nd_order, _quadrature]]

16839

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _quadrature]]

16840

\[ {}y^{\prime \prime } = 2 \ln \left (x \right ) x \]

[[_2nd_order, _quadrature]]

16841

\[ {}x y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_y]]

16842

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

16843

\[ {}x y^{\prime \prime } = \left (2 x^{2}+1\right ) y^{\prime } \]

[[_2nd_order, _missing_y]]

16844

\[ {}x y^{\prime \prime } = y^{\prime }+x^{2} \]

[[_2nd_order, _missing_y]]

16856

\[ {}y^{\prime \prime }+y^{\prime }+2 = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16873

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

16874

\[ {}3 y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

[[_2nd_order, _missing_x]]

16876

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16877

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16879

\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

16881

\[ {}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

16884

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16885

\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16895

\[ {}y^{\prime \prime }+3 y^{\prime } = 3 \]

[[_2nd_order, _missing_x]]

16896

\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \]

[[_2nd_order, _missing_y]]

16897

\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

16898

\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \]

[[_2nd_order, _missing_y]]

16899

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16900

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

16901

\[ {}4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}} \]

[[_2nd_order, _missing_y]]

16902

\[ {}y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x} \]

[[_2nd_order, _missing_y]]

16903

\[ {}y^{\prime \prime }+25 y = \cos \left (5 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16904

\[ {}y^{\prime \prime }+y = \sin \left (x \right )-\cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16905

\[ {}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16906

\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16907

\[ {}y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16908

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16909

\[ {}y^{\prime \prime }+k^{2} y = k \sin \left (k x +\alpha \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16910

\[ {}y^{\prime \prime }+k^{2} y = k \]

[[_2nd_order, _missing_x]]

16931

\[ {}y^{\prime \prime }+2 y^{\prime }+y = -2 \]

[[_2nd_order, _missing_x]]

16932

\[ {}y^{\prime \prime }+2 y^{\prime } = -2 \]

[[_2nd_order, _missing_x]]

16933

\[ {}y^{\prime \prime }+9 y = 9 \]

[[_2nd_order, _missing_x]]

16939

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

16940

\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \]

[[_2nd_order, _missing_y]]

16941

\[ {}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

16942

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

16943

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

16944

\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \]

[[_2nd_order, _missing_y]]

16945

\[ {}y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _missing_y]]

16946

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16947

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = x +1 \]

[[_2nd_order, _with_linear_symmetries]]

16948

\[ {}y^{\prime \prime }+y^{\prime }+y = \left (x^{2}+x \right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16949

\[ {}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16950

\[ {}y^{\prime \prime }+y = 4 x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16951

\[ {}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \sin \left (n x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16952

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16953

\[ {}y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16954

\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

16955

\[ {}y^{\prime \prime }+2 y^{\prime } = 4 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \]

[[_2nd_order, _missing_y]]

16956

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16957

\[ {}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

16958

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16959

\[ {}y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16960

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16963

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16965

\[ {}y^{\prime \prime }+y = x^{2} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16966

\[ {}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16970

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16971

\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16972

\[ {}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x} \]

[[_2nd_order, _missing_y]]

16973

\[ {}y^{\prime \prime }-y = x +\sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16974

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (\sin \left (x \right )+1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16977

\[ {}y^{\prime \prime }+4 y = \sin \left (x \right ) \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16978

\[ {}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2} \]

[[_2nd_order, _missing_y]]

16979

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

16980

\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \]

[[_2nd_order, _missing_y]]

16981

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16982

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16983

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16984

\[ {}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16985

\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16987

\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \]

[[_2nd_order, _missing_y]]

16989

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16990

\[ {}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

16991

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16992

\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

16993

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16994

\[ {}y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16995

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16996

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16997

\[ {}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \]

[[_2nd_order, _missing_y]]

16998

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

16999

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x +\sin \left (x \right )+\sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17000

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17001

\[ {}y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17002

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17003

\[ {}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right ) \]

[[_2nd_order, _missing_y]]

17005

\[ {}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17010

\[ {}y^{\prime \prime }+y = -2 x +2 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17011

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17012

\[ {}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17013

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17014

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17015

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _missing_y]]

17016

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17017

\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17018

\[ {}y^{\prime \prime }+4 y = \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17019

\[ {}y^{\prime \prime }+y = 4 x \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17020

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17021

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17022

\[ {}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \]
i.c.

[[_2nd_order, _missing_y]]

17023

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17028

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17029

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17030

\[ {}y^{\prime \prime }-y = 1 \]

[[_2nd_order, _missing_x]]

17031

\[ {}y^{\prime \prime }-y = -2 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17038

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17039

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17040

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0 \]

[[_Emden, _Fowler]]

17041

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

17042

\[ {}\left (2+x \right )^{2} y^{\prime \prime }+3 \left (2+x \right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

17043

\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

17048

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right ) \]

[[_2nd_order, _with_linear_symmetries]]

17049

\[ {}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17050

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17051

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2 \]

[[_2nd_order, _with_linear_symmetries]]

17052

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17053

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17054

\[ {}\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y = 6 \ln \left (x +1\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17055

\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-3 \left (-2+x \right ) y^{\prime }+4 y = x \]

[[_2nd_order, _with_linear_symmetries]]

17056

\[ {}\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

17057

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0 \]

[_Jacobi]

17058

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y = 6 \]

[[_2nd_order, _with_linear_symmetries]]

17069

\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17070

\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1} \]

[[_2nd_order, _missing_y]]

17071

\[ {}y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17072

\[ {}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17073

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17074

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17075

\[ {}y^{\prime \prime }+y = \frac {2}{\sin \left (x \right )^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17076

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \]

[[_2nd_order, _missing_y]]

17078

\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}} \]

[[_2nd_order, _missing_y]]

17079

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1 \]

[[_2nd_order, _missing_y]]

17081

\[ {}x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2} \]

[[_2nd_order, _missing_y]]

17085

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1} \]
i.c.

[[_2nd_order, _missing_y]]

17091

\[ {}x^{\prime \prime }+x^{\prime }+x = 0 \]

[[_2nd_order, _missing_x]]

17092

\[ {}x^{\prime \prime }+2 x^{\prime }+6 x = 0 \]

[[_2nd_order, _missing_x]]

17093

\[ {}x^{\prime \prime }+2 x^{\prime }+x = 0 \]

[[_2nd_order, _missing_x]]

17101

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17102

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17103

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17106

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17107

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17108

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17109

\[ {}y^{\prime \prime }+\alpha y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17110

\[ {}y^{\prime \prime }+\alpha ^{2} y = 1 \]
i.c.

[[_2nd_order, _missing_x]]

17111

\[ {}y^{\prime \prime }+y = 1 \]
i.c.

[[_2nd_order, _missing_x]]

17112

\[ {}y^{\prime \prime }+\lambda ^{2} y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17113

\[ {}y^{\prime \prime }+\lambda ^{2} y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17116

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

17138

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

17142

\[ {}x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

17145

\[ {}y^{\prime \prime }+4 y = \cos \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17146

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \pi ^{2}-x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

17147

\[ {}y^{\prime \prime }-4 y = \cos \left (\pi x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17148

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \arcsin \left (\sin \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17149

\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17472

\[ {}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d \]

[[_2nd_order, _with_linear_symmetries]]

17473

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17474

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17475

\[ {}y^{\prime \prime }+y^{\prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17476

\[ {}y^{\prime \prime }+3 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17477

\[ {}y^{\prime \prime }-y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17484

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {\alpha \left (1+\alpha \right ) \mu ^{2} y}{-x^{2}+1} = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

17486

\[ {}t^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17488

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

17489

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

17490

\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

17492

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

17504

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

17505

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

17506

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

17507

\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

17508

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

17509

\[ {}y^{\prime \prime }-2 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

17510

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

17511

\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

17512

\[ {}6 y^{\prime \prime }-y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

17513

\[ {}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

17514

\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 0 \]

[[_2nd_order, _missing_x]]

17515

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

17516

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

17517

\[ {}4 y^{\prime \prime }-9 y = 0 \]

[[_2nd_order, _missing_x]]

17518

\[ {}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

17519

\[ {}y^{\prime \prime }-4 y^{\prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

17520

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

17521

\[ {}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0 \]

[[_2nd_order, _missing_x]]

17522

\[ {}y^{\prime \prime }-9 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

17523

\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

17524

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

17525

\[ {}9 y^{\prime \prime }-24 y^{\prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

17526

\[ {}4 y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

17527

\[ {}4 y^{\prime \prime }+9 y^{\prime }-9 y = 0 \]

[[_2nd_order, _missing_x]]

17528

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0 \]

[[_2nd_order, _missing_x]]

17529

\[ {}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0 \]

[[_2nd_order, _missing_x]]

17530

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17531

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17532

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17533

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17534

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17535

\[ {}6 y^{\prime \prime }-5 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17536

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17537

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17538

\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17539

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17540

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17541

\[ {}y^{\prime \prime }+6 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17542

\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17543

\[ {}2 y^{\prime \prime }+y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17544

\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17545

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17546

\[ {}4 y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17547

\[ {}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = 0 \]

[[_Emden, _Fowler]]

17548

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

17549

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17550

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\frac {5 y}{4} = 0 \]

[[_Emden, _Fowler]]

17551

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }-6 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17552

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

17553

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

17554

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler]]

17555

\[ {}2 x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

[[_Emden, _Fowler]]

17556

\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

17557

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 y = 0 \]
i.c.

[[_Emden, _Fowler]]

17558

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]
i.c.

[[_Emden, _Fowler]]

17559

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0 \]
i.c.

[[_Emden, _Fowler]]

17560

\[ {}y^{\prime \prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17561

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17562

\[ {}m y^{\prime \prime }+k y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17563

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 3 \,{\mathrm e}^{2 t} \]

[[_2nd_order, _with_linear_symmetries]]

17564

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17565

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = -3 t \,{\mathrm e}^{-t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17566

\[ {}y^{\prime \prime }+2 y^{\prime } = 3+4 \sin \left (2 t \right ) \]

[[_2nd_order, _missing_y]]

17567

\[ {}y^{\prime \prime }+9 y = t^{2} {\mathrm e}^{3 t}+6 \]

[[_2nd_order, _linear, _nonhomogeneous]]

17568

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

17569

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 2 \,{\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

17570

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

17571

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

17572

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \]

[[_2nd_order, _with_linear_symmetries]]

17573

\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = t^{2}+3 \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17574

\[ {}y^{\prime \prime }+y = 3 \sin \left (2 t \right )+t \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17575

\[ {}u^{\prime \prime }+w_{0}^{2} u = \cos \left (w t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17576

\[ {}y^{\prime \prime }+y^{\prime }+4 y = 2 \sinh \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17577

\[ {}y^{\prime \prime }-y^{\prime }-2 y = \cosh \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17578

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 2 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17579

\[ {}y^{\prime \prime }+4 y = t^{2}+3 \,{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17580

\[ {}y^{\prime \prime }-2 y^{\prime }+y = t \,{\mathrm e}^{t}+4 \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17581

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 3 t \,{\mathrm e}^{2 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17582

\[ {}y^{\prime \prime }+4 y = 3 \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17583

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17584

\[ {}y^{\prime \prime }+3 y^{\prime } = 2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right ) \]

[[_2nd_order, _missing_y]]

17585

\[ {}y^{\prime \prime }+y = t \left (1+\sin \left (t \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17586

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17587

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17588

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 t^{2}+4 t \,{\mathrm e}^{2 t}+t \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17589

\[ {}y^{\prime \prime }+4 y = t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17590

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17591

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 t \,{\mathrm e}^{-t} \cos \left (2 t \right )-2 t \,{\mathrm e}^{-2 t} \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17592

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 2 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

17593

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

17594

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17595

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 x^{2}+2 \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

17596

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17597

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{-t +\pi } & \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17598

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17599

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17600

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 2 \cos \left (w t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17601

\[ {}y^{\prime \prime }+y = 2 \cos \left (w t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17602

\[ {}y^{\prime \prime }+y = 3 \cos \left (w t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17603

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (\frac {t}{4}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17604

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17605

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (6 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17608

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

17609

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

17610

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

17611

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \]

[[_2nd_order, _with_linear_symmetries]]

17612

\[ {}y^{\prime \prime }+y = \tan \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17613

\[ {}y^{\prime \prime }+4 y = 3 \sec \left (2 t \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17614

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17615

\[ {}y^{\prime \prime }+4 y = 2 \csc \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17616

\[ {}4 y^{\prime \prime }+y = 2 \sec \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17617

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17618

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17619

\[ {}y^{\prime \prime }+4 y = g \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17620

\[ {}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3} \]

[[_2nd_order, _with_linear_symmetries]]

17621

\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t} \]

[[_2nd_order, _with_linear_symmetries]]

17622

\[ {}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

17623

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 3 x^{{3}/{2}} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17624

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = g \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

17625

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17626

\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17627

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17628

\[ {}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

17629

\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17630

\[ {}y^{\prime \prime }+y = g \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17814

\[ {}y^{\prime \prime } = \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

17917

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0 \]

[_Lienard]

17922

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

17923

\[ {}y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = -1+x \]

[[_2nd_order, _with_linear_symmetries]]

17926

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

17928

\[ {}y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y = 0 \]

[[_2nd_order, _missing_x]]

17929

\[ {}\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

17935

\[ {}2 y^{\prime \prime }+y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

17937

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

17938

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17941

\[ {}y^{\prime \prime }+4 y = x \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17942

\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17943

\[ {}y^{\prime \prime }-y = \frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17944

\[ {}y^{\prime \prime }-2 y = 4 x^{2} {\mathrm e}^{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17945

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17946

\[ {}y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17947

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

17948

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x \]

[[_2nd_order, _with_linear_symmetries]]

17949

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = \ln \left (x \right ) x \]

[[_2nd_order, _with_linear_symmetries]]

17950

\[ {}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

17952

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17954

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0 \]

[_Lienard]

17956

\[ {}x y^{\prime \prime }-y^{\prime }-x^{3} y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

17957

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17958

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

17981

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

17982

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

18022

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

18114

\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \]

[[_2nd_order, _missing_y]]

18135

\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \]

[[_2nd_order, _missing_y]]

18142

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

18170

\[ {}x y^{\prime \prime }-y^{\prime } = 3 x^{2} \]

[[_2nd_order, _missing_y]]

18171

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

18172

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x \]

[[_2nd_order, _with_linear_symmetries]]

18173

\[ {}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 1 \]

[[_2nd_order, _with_linear_symmetries]]

18174

\[ {}y^{\prime \prime }-2 y^{\prime } = 6 \]

[[_2nd_order, _missing_x]]

18175

\[ {}y^{\prime \prime }-2 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18176

\[ {}y^{\prime \prime } = {\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

18177

\[ {}y^{\prime \prime }-2 y^{\prime } = 4 \]

[[_2nd_order, _missing_x]]

18178

\[ {}y^{\prime \prime }-y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18179

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18180

\[ {}y^{\prime \prime }+2 y^{\prime } = 6 \,{\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

18181

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18182

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18183

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

18184

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]
i.c.

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18185

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18186

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

18187

\[ {}x^{2} y^{\prime \prime }-2 y = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

18188

\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18189

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18190

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18192

\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18205

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

18206

\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \]

[_Laguerre]

18207

\[ {}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0 \]

[_Laguerre]

18209

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

18210

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

18211

\[ {}y^{\prime \prime }+8 y = 0 \]

[[_2nd_order, _missing_x]]

18212

\[ {}2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \]

[[_2nd_order, _missing_x]]

18213

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

18214

\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 0 \]

[[_2nd_order, _missing_x]]

18215

\[ {}2 y^{\prime \prime }+2 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

18216

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

18217

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

18218

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

18219

\[ {}4 y^{\prime \prime }+20 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

18220

\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

18221

\[ {}y^{\prime \prime } = 4 y \]

[[_2nd_order, _missing_x]]

18222

\[ {}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \]

[[_2nd_order, _missing_x]]

18223

\[ {}2 y^{\prime \prime }+y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

18224

\[ {}16 y^{\prime \prime }-8 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

18225

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

18226

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 0 \]

[[_2nd_order, _missing_x]]

18227

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18228

\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18229

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18230

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18231

\[ {}y^{\prime \prime }+4 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18232

\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18233

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

[[_Emden, _Fowler]]

18234

\[ {}2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

[[_Emden, _Fowler]]

18235

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

[[_Emden, _Fowler]]

18236

\[ {}4 x^{2} y^{\prime \prime }-3 y = 0 \]

[[_Emden, _Fowler]]

18237

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18238

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18239

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y = 0 \]

[[_Emden, _Fowler]]

18240

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-2 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18241

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18242

\[ {}x y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }+x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18244

\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

18245

\[ {}y^{\prime \prime }+4 y = 3 \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18246

\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \]

[[_2nd_order, _with_linear_symmetries]]

18247

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \]

[[_2nd_order, _with_linear_symmetries]]

18248

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

18249

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18250

\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18251

\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

[[_2nd_order, _missing_y]]

18252

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

18253

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18254

\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

[[_2nd_order, _missing_y]]

18255

\[ {}y^{\prime \prime }+k^{2} y = \sin \left (b x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18256

\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \]

[[_2nd_order, _linear, _nonhomogeneous]]

18257

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18258

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \]

[[_2nd_order, _with_linear_symmetries]]

18259

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

18260

\[ {}y^{\prime \prime }+4 y = \tan \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18261

\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18262

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18263

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18264

\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

18265

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18266

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18267

\[ {}y^{\prime \prime }+y = \cot \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18268

\[ {}y^{\prime \prime }+y = \cot \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18269

\[ {}y^{\prime \prime }+y = x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18270

\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18271

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18272

\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18273

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

18274

\[ {}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y = x \left (x +1\right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18275

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

18276

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

18277

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

18301

\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

18302

\[ {}y^{\prime \prime }-y = x^{2} {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18303

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18304

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

18305

\[ {}y^{\prime \prime }-y = {\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

18306

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

18307

\[ {}y^{\prime \prime }-y^{\prime }+y = x^{3}-3 x^{2}+1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

18309

\[ {}4 y^{\prime \prime }+y = x^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18312

\[ {}y^{\prime \prime }+y^{\prime }-y = -x^{4}+3 x \]

[[_2nd_order, _linear, _nonhomogeneous]]

18313

\[ {}y^{\prime \prime }+y = x^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18316

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18317

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18318

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18327

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18335

\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18434

\[ {}t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0 \]

[[_Emden, _Fowler]]

18437

\[ {}t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18438

\[ {}x^{\prime \prime }-5 x^{\prime }+6 x = 0 \]

[[_2nd_order, _missing_x]]

18439

\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = 0 \]

[[_2nd_order, _missing_x]]

18440

\[ {}x^{\prime \prime }-4 x^{\prime }+5 x = 0 \]

[[_2nd_order, _missing_x]]

18441

\[ {}x^{\prime \prime }+3 x^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

18442

\[ {}x^{\prime \prime }-3 x^{\prime }+2 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18443

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18444

\[ {}x^{\prime \prime }+2 x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18445

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18446

\[ {}x^{\prime \prime }-x = t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

18447

\[ {}x^{\prime \prime }-x = {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

18448

\[ {}x^{\prime \prime }+2 x^{\prime }+4 x = {\mathrm e}^{t} \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

18449

\[ {}x^{\prime \prime }-x^{\prime }+x = \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

18450

\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = t \sin \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

18451

\[ {}x^{\prime \prime }+x = \cos \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

18486

\[ {}\theta ^{\prime \prime } = -p^{2} \theta \]

[[_2nd_order, _missing_x]]

18501

\[ {}\theta ^{\prime \prime }-p^{2} \theta = 0 \]

[[_2nd_order, _missing_x]]

18502

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

18503

\[ {}y^{\prime \prime }+12 y = 7 y^{\prime } \]

[[_2nd_order, _missing_x]]

18504

\[ {}r^{\prime \prime }-a^{2} r = 0 \]

[[_2nd_order, _missing_x]]

18506

\[ {}v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u} \]

[[_2nd_order, _with_linear_symmetries]]

18507

\[ {}y^{\prime \prime }+4 y^{\prime }-y = \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18508

\[ {}y^{\prime \prime }+3 y = \sin \left (x \right )+\frac {\sin \left (3 x \right )}{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18516

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18520

\[ {}y^{\prime \prime } = -m^{2} y \]

[[_2nd_order, _missing_x]]

18523

\[ {}x y^{\prime \prime }+2 y^{\prime } = x y \]

[[_2nd_order, _with_linear_symmetries]]

18527

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x} \]

[[_2nd_order, _with_linear_symmetries]]

18528

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

18529

\[ {}v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

[[_2nd_order, _missing_y]]

18536

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18537

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

18539

\[ {}v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18576

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

18577

\[ {}y^{\prime \prime }+2 y^{\prime }-2 y = 0 \]

[[_2nd_order, _missing_x]]

18585

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

18587

\[ {}y^{\prime \prime }-4 y^{\prime }+2 y = x \]

[[_2nd_order, _with_linear_symmetries]]

18588

\[ {}y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

18591

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

18592

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

18593

\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18595

\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18599

\[ {}e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2} \]

[[_2nd_order, _quadrature]]

18600

\[ {}e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \]

[[_2nd_order, _quadrature]]

18601

\[ {}e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \]

[[_2nd_order, _quadrature]]

18602

\[ {}e y^{\prime \prime } = -P \left (L -x \right ) \]

[[_2nd_order, _quadrature]]

18603

\[ {}e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \]

[[_2nd_order, _quadrature]]

18604

\[ {}e y^{\prime \prime } = P \left (-y+a \right ) \]

[[_2nd_order, _missing_x]]

18606

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = x \]

[[_2nd_order, _with_linear_symmetries]]

18610

\[ {}x y^{\prime \prime }+2 y^{\prime } = 2 x \]

[[_2nd_order, _missing_y]]

18611

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

18612

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18613

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18615

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18616

\[ {}\left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18619

\[ {}y^{\prime \prime } = \cos \left (x \right ) \]

[[_2nd_order, _quadrature]]

18620

\[ {}x^{2} y^{\prime \prime } = \ln \left (x \right ) \]

[[_2nd_order, _quadrature]]

18621

\[ {}y^{\prime \prime } = -a^{2} y \]

[[_2nd_order, _missing_x]]

18626

\[ {}x y^{\prime \prime }+3 y^{\prime } = 3 x \]

[[_2nd_order, _missing_y]]

18627

\[ {}x = y^{\prime \prime }+y^{\prime } \]

[[_2nd_order, _missing_y]]

18630

\[ {}V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0 \]

[[_2nd_order, _missing_y]]

18631

\[ {}V^{\prime \prime }+\frac {V^{\prime }}{r} = 0 \]

[[_2nd_order, _missing_y]]

18645

\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18646

\[ {}v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

[[_2nd_order, _missing_y]]

18647

\[ {}y^{\prime \prime }-k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

18788

\[ {}y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

[[_2nd_order, _missing_x]]

18789

\[ {}y^{\prime \prime }-m^{2} y = 0 \]

[[_2nd_order, _missing_x]]

18790

\[ {}2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

[[_2nd_order, _missing_x]]

18791

\[ {}9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

[[_2nd_order, _missing_x]]

18794

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

18797

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

18798

\[ {}y^{\prime \prime }-y = 2+5 x \]

[[_2nd_order, _with_linear_symmetries]]

18799

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

18803

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}} \]

[[_2nd_order, _with_linear_symmetries]]

18807

\[ {}y^{\prime \prime }+a^{2} y = \cos \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18808

\[ {}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18811

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18812

\[ {}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18813

\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18814

\[ {}y^{\prime \prime }-y = x^{2} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18818

\[ {}y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18819

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x} \]

[[_2nd_order, _with_linear_symmetries]]

18820

\[ {}y^{\prime \prime }-a^{2} y = {\mathrm e}^{a x}+{\mathrm e}^{n x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18826

\[ {}y^{\prime \prime }+a^{2} y = \sec \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18827

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18828

\[ {}y^{\prime \prime }+n^{2} y = {\mathrm e}^{x} x^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18832

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18834

\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18838

\[ {}y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18839

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18841

\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 20 x \]

[[_2nd_order, _with_linear_symmetries]]

18844

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

18845

\[ {}x^{2} y^{\prime \prime }+y = 3 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

18848

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18849

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4} \]

[[_2nd_order, _with_linear_symmetries]]

18850

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (x +1\right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

18851

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18853

\[ {}\left (2 x -1\right )^{3} y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18855

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18857

\[ {}\left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x \]

[[_2nd_order, _with_linear_symmetries]]

18861

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18862

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m} \]

[[_2nd_order, _with_linear_symmetries]]

18865

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18866

\[ {}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18867

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18869

\[ {}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5 \]

[[_2nd_order, _linear, _nonhomogeneous]]

18870

\[ {}x y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18877

\[ {}y^{\prime \prime } = x^{2} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

18878

\[ {}y^{\prime \prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

18895

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

18904

\[ {}y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )} \]

[[_2nd_order, _missing_y]]

18911

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2 \]

[[_2nd_order, _missing_y]]

18914

\[ {}y^{\prime \prime } = \frac {a}{x} \]

[[_2nd_order, _quadrature]]

18917

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

18920

\[ {}a y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

18924

\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

18925

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x \]

[[_2nd_order, _with_linear_symmetries]]

18926

\[ {}\left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18927

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18928

\[ {}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18931

\[ {}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18932

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18933

\[ {}x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18934

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18936

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18938

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = n^{2} y \]

[[_2nd_order, _with_linear_symmetries]]

18939

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18940

\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18941

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

18944

\[ {}y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

18946

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}} \]

[[_2nd_order, _with_linear_symmetries]]

18950

\[ {}y^{\prime \prime }+x y^{\prime }-y = f \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

18951

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

18952

\[ {}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18953

\[ {}\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18956

\[ {}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

18966

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x} \]

[[_2nd_order, _with_linear_symmetries]]

18967

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{r} = 0 \]

[[_2nd_order, _missing_y]]

19080

\[ {}y^{\prime \prime }-n^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19082

\[ {}2 x^{\prime \prime }+5 x^{\prime }-12 x = 0 \]

[[_2nd_order, _missing_x]]

19083

\[ {}y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

[[_2nd_order, _missing_x]]

19084

\[ {}9 x^{\prime \prime }+18 x^{\prime }-16 x = 0 \]

[[_2nd_order, _missing_x]]

19086

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

19094

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

19095

\[ {}y^{\prime \prime }-y = 2+5 x \]

[[_2nd_order, _with_linear_symmetries]]

19096

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

19097

\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19098

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}} \]

[[_2nd_order, _with_linear_symmetries]]

19099

\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

19100

\[ {}y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x} \]

[[_2nd_order, _with_linear_symmetries]]

19101

\[ {}y^{\prime \prime }+9 y = \sin \left (2 x \right )+\cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19102

\[ {}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )+\cos \left (b x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19103

\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{x}+\sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19105

\[ {}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19106

\[ {}y^{\prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19112

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19113

\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19114

\[ {}y^{\prime \prime }-y = \cosh \left (x \right ) \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19117

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \left (-1+x \right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19118

\[ {}y^{\prime \prime }+2 y^{\prime }+y = x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19121

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19122

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19123

\[ {}y^{\prime \prime }+y = {\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19127

\[ {}y^{\prime \prime }+y = 3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19130

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0 \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

19236

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[[_Emden, _Fowler]]

19237

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right ) \]

[[_2nd_order, _with_linear_symmetries]]

19244

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0 \]

[[_Emden, _Fowler]]

19246

\[ {}x^{2} y^{\prime \prime }+y = 3 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

19247

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19248

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{4} \]

[[_2nd_order, _with_linear_symmetries]]

19249

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \]

[[_2nd_order, _with_linear_symmetries]]

19250

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = x^{4} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19251

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19252

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{m} \]

[[_2nd_order, _with_linear_symmetries]]

19253

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime } = \ln \left (x \right ) \]

[[_2nd_order, _missing_y]]

19254

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19255

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = x \]

[[_2nd_order, _with_linear_symmetries]]

19259

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (x +1\right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

19262

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = \ln \left (x \right ) x \]

[[_2nd_order, _with_linear_symmetries]]

19263

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = x^{2} \sin \left (\ln \left (x \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19266

\[ {}\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19267

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime } = \left (2 x +3\right ) \left (2 x +4\right ) \]

[[_2nd_order, _missing_y]]

19268

\[ {}x y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19270

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19274

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19275

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19276

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 2 x \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19277

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = \left (x +1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19279

\[ {}\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19284

\[ {}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5 \]

[[_2nd_order, _linear, _nonhomogeneous]]

19287

\[ {}y^{\prime \prime } = x +\sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

19288

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

19289

\[ {}y^{\prime \prime } \cos \left (x \right )^{2} = 1 \]

[[_2nd_order, _quadrature]]

19291

\[ {}y^{\prime \prime } = \frac {a}{x} \]

[[_2nd_order, _quadrature]]

19293

\[ {}y^{\prime \prime } \sqrt {a^{2}+x^{2}} = x \]

[[_2nd_order, _quadrature]]

19294

\[ {}x^{2} y^{\prime \prime } = \ln \left (x \right ) \]

[[_2nd_order, _quadrature]]

19295

\[ {}y^{\prime \prime } = y \]

[[_2nd_order, _missing_x]]

19297

\[ {}y^{\prime \prime }-a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19301

\[ {}y^{\prime \prime } = x y^{\prime } \]

[[_2nd_order, _missing_y]]

19303

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

19304

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0 \]

[[_2nd_order, _missing_y]]

19306

\[ {}y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )} \]

[[_2nd_order, _missing_y]]

19307

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a x = 0 \]

[[_2nd_order, _missing_y]]

19308

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = a x \]

[[_2nd_order, _missing_y]]

19312

\[ {}x y^{\prime \prime }+y^{\prime } = x \]

[[_2nd_order, _missing_y]]

19313

\[ {}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0 \]

[[_2nd_order, _missing_y]]

19321

\[ {}a y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

19343

\[ {}y^{\prime \prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19348

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19351

\[ {}{\mathrm e}^{x} \left (x y^{\prime \prime }-y^{\prime }\right ) = x^{3} \]

[[_2nd_order, _missing_y]]

19352

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2 \]

[[_2nd_order, _missing_y]]

19356

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x \]

[[_2nd_order, _with_linear_symmetries]]

19357

\[ {}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0 \]

[_Laguerre]

19358

\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime } = y+{\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19359

\[ {}\left (x +1\right ) y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }+\left (x +5\right ) y = {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19360

\[ {}\left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19361

\[ {}y^{\prime \prime }+x y^{\prime }-y = X \]

[[_2nd_order, _with_linear_symmetries]]

19367

\[ {}y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19368

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19369

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = n^{2} y \]

[[_2nd_order, _with_linear_symmetries]]

19370

\[ {}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19371

\[ {}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x \]

[[_2nd_order, _linear, _nonhomogeneous]]

19373

\[ {}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19374

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = \sec \left (x \right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19375

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19376

\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19377

\[ {}y^{\prime \prime }+2 n \cot \left (n x \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19378

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19379

\[ {}x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19380

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19382

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19383

\[ {}\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19384

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+m^{2} y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19387

\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19390

\[ {}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19391

\[ {}x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-2 y = x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19392

\[ {}x^{2} y^{\prime \prime }+y^{\prime }-\left (x^{2}+1\right ) y = {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19393

\[ {}\left (2+x \right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (x +1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

19394

\[ {}y^{\prime \prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

19395

\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19396

\[ {}y^{\prime \prime }+4 y = 4 \tan \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19397

\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \]

[[_2nd_order, _with_linear_symmetries]]

19398

\[ {}y^{\prime \prime }-y = \frac {2}{{\mathrm e}^{x}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19399

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }-\left (x^{2}+1\right ) y = x \]

[[_2nd_order, _linear, _nonhomogeneous]]

19400

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = -4 x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

19401

\[ {}-y+x y^{\prime } = \left (-1+x \right ) \left (y^{\prime \prime }-x +1\right ) \]

[[_2nd_order, _with_linear_symmetries]]

19403

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]

19404

\[ {}\left (x^{2}+a \right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19405

\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19406

\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = x^{3}+3 x \]

[[_2nd_order, _with_linear_symmetries]]

19407

\[ {}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19408

\[ {}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0 \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19409

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {a^{2} y}{-x^{2}+1} = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19410

\[ {}\left (2 x -1\right ) y^{\prime \prime }-2 y^{\prime }+\left (3-2 x \right ) y = 2 \,{\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19411

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 8 x^{3} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19412

\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+5\right ) y = x \,{\mathrm e}^{-\frac {x^{2}}{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19413

\[ {}x \left (-x^{2}+1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) \left (3 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19414

\[ {}y^{\prime \prime }+\left (1-\frac {2}{x^{2}}\right ) y = x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19415

\[ {}\left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19416

\[ {}x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y = \left (-2+x \right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19417

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

19419

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0 \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19421

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19422

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y = {\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

19423

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime } = m^{2} y \]

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

19426

\[ {}\left (2+x \right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (x +1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

19427

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}} \]

[[_2nd_order, _with_linear_symmetries]]

19428

\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19450

\[ {}2 y^{\prime \prime }+9 y^{\prime }-18 y = 0 \]

[[_2nd_order, _missing_x]]

19454

\[ {}y^{\prime \prime }+n^{2} y = \sec \left (n x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19456

\[ {}y^{\prime \prime }-4 y^{\prime }+y = a \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19459

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19461

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19462

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \sinh \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19463

\[ {}y^{\prime \prime }+a^{2} y = \cos \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19464

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19500

\[ {}x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19504

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 2 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

19506

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19508

\[ {}\left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x \]

[[_2nd_order, _with_linear_symmetries]]

19510

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19512

\[ {}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19513

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19518

\[ {}2 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (7 x +3\right ) y^{\prime }-3 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

19524

\[ {}y^{\prime \prime } = x^{2} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

19525

\[ {}y^{\prime \prime } = \sec \left (x \right )^{2} \]

[[_2nd_order, _quadrature]]

19531

\[ {}x y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

19535

\[ {}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19537

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}} \]

[[_2nd_order, _with_linear_symmetries]]

19538

\[ {}\left (2+x \right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (x +1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

19542

\[ {}x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19543

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19544

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19545

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+y = 0 \]

[_Lienard]

19546

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19550

\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19552

\[ {}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19553

\[ {}x y^{\prime \prime }+\left (-1+x \right ) y^{\prime }-y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

19554

\[ {}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

19555

\[ {}y^{\prime \prime }+a^{2} y = \sec \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19556

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

19557

\[ {}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3} \]

[[_2nd_order, _with_linear_symmetries]]