2.4.2 second order linear constant coeff

Table 2.455: second order linear constant coeff

#

ODE

ODE 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

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

[[_2nd_order, _quadrature]]

16

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

[[_2nd_order, _quadrature]]

17

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

[[_2nd_order, _quadrature]]

18

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

[[_2nd_order, _quadrature]]

149

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

[[_2nd_order, _missing_x]]

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]]

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]]

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]]

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]]

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

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

[[_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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

2402

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

[[_2nd_order, _linear, _nonhomogeneous]]

2403

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

[[_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

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

[[_2nd_order, _linear, _nonhomogeneous]]

2409

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

[[_2nd_order, _linear, _nonhomogeneous]]

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]]

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]]

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]]

2583

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

[[_2nd_order, _linear, _nonhomogeneous]]

2584

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

[[_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

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

[[_2nd_order, _linear, _nonhomogeneous]]

2590

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

[[_2nd_order, _linear, _nonhomogeneous]]

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

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

[[_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]]

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]]

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]]

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]]

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]]

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]]

3570

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

[[_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]]

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]]

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]]

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]]

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]]

4141

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

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

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

[[_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]]

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]]

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

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

[[_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]]

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]]

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]]

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]]

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]]

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]]

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]]

6573

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

[[_2nd_order, _missing_x]]

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

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

[[_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]]

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]]

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]]

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]]

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]]

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]]

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]]

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]]

7581

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

[[_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]]

7759

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

[[_2nd_order, _missing_x]]

7762

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

[[_2nd_order, _missing_x]]

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]]

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]]

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]]

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

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

[[_2nd_order, _linear, _nonhomogeneous]]

8062

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

[[_2nd_order, _linear, _nonhomogeneous]]

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]]

8307

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

[[_2nd_order, _missing_x]]

8500

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

[[_2nd_order, _missing_x]]

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]]

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]]

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]]

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]]

8960

\[ {}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

8977

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (x +2\right ) {\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

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]]

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]]

12422

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

[[_2nd_order, _missing_x]]

12848

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

[[_2nd_order, _missing_x]]

12849

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

[[_2nd_order, _missing_x]]

12859

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

[[_2nd_order, _linear, _nonhomogeneous]]

12861

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

[[_2nd_order, _linear, _nonhomogeneous]]

12862

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

[[_2nd_order, _with_linear_symmetries]]

12864

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

[[_2nd_order, _linear, _nonhomogeneous]]

12866

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

[[_2nd_order, _linear, _nonhomogeneous]]

12867

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

[[_2nd_order, _linear, _nonhomogeneous]]

12868

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

[[_2nd_order, _linear, _nonhomogeneous]]

12869

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

[[_2nd_order, _linear, _nonhomogeneous]]

12870

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

[[_2nd_order, _linear, _nonhomogeneous]]

12871

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

[[_2nd_order, _linear, _nonhomogeneous]]

12875

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

[[_2nd_order, _missing_y]]

12881

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

[[_2nd_order, _linear, _nonhomogeneous]]

12883

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

[[_2nd_order, _linear, _nonhomogeneous]]

12888

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

[[_2nd_order, _linear, _nonhomogeneous]]

12889

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

[[_2nd_order, _linear, _nonhomogeneous]]

12891

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

[[_2nd_order, _linear, _nonhomogeneous]]

12920

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

[[_2nd_order, _quadrature]]

12957

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

[[_2nd_order, _missing_x]]

12962

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

[[_2nd_order, _missing_x]]

12967

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

[[_2nd_order, _quadrature]]

13025

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

[[_2nd_order, _missing_y]]

13041

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

[[_2nd_order, _missing_x]]

13042

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

[[_2nd_order, _missing_x]]

13043

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

[[_2nd_order, _missing_x]]

13044

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

[[_2nd_order, _missing_x]]

13045

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

[[_2nd_order, _missing_x]]

13046

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

[[_2nd_order, _missing_x]]

13047

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

[[_2nd_order, _missing_x]]

13048

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

[[_2nd_order, _missing_x]]

13049

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

[[_2nd_order, _missing_x]]

13050

\[ {}x^{\prime \prime }-4 x^{\prime }+6 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13051

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

[[_2nd_order, _missing_x]]

13052

\[ {}x^{\prime \prime }-12 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13053

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

[[_2nd_order, _missing_x]]

13054

\[ {}\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13055

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

[[_2nd_order, _missing_x]]

13056

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

[[_2nd_order, _missing_x]]

13057

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

[[_2nd_order, _linear, _nonhomogeneous]]

13058

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

[[_2nd_order, _linear, _nonhomogeneous]]

13059

\[ {}x^{\prime \prime }+x^{\prime }+x = 12 \]

[[_2nd_order, _missing_x]]

13060

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

[[_2nd_order, _linear, _nonhomogeneous]]

13061

\[ {}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13062

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

[[_2nd_order, _linear, _nonhomogeneous]]

13063

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

[[_2nd_order, _linear, _nonhomogeneous]]

13064

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

[[_2nd_order, _linear, _nonhomogeneous]]

13065

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

[[_2nd_order, _with_linear_symmetries]]

13066

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

[[_2nd_order, _linear, _nonhomogeneous]]

13067

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

[[_2nd_order, _linear, _nonhomogeneous]]

13068

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

[[_2nd_order, _linear, _nonhomogeneous]]

13069

\[ {}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13070

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

[[_2nd_order, _missing_y]]

13071

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

[[_2nd_order, _with_linear_symmetries]]

13072

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

[[_2nd_order, _with_linear_symmetries]]

13073

\[ {}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

13074

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

[[_2nd_order, _linear, _nonhomogeneous]]

13075

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

[[_2nd_order, _linear, _nonhomogeneous]]

13077

\[ {}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13078

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

[[_2nd_order, _missing_x]]

13079

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

[[_2nd_order, _linear, _nonhomogeneous]]

13080

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13081

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

[[_2nd_order, _linear, _nonhomogeneous]]

13082

\[ {}x^{\prime \prime }+3025 x = \cos \left (45 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13092

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

[[_2nd_order, _linear, _nonhomogeneous]]

13093

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

[[_2nd_order, _linear, _nonhomogeneous]]

13094

\[ {}x^{\prime \prime }-x = \frac {1}{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13096

\[ {}x^{\prime \prime }+x = \frac {1}{1+t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13097

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

[[_2nd_order, _linear, _nonhomogeneous]]

13100

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

[[_2nd_order, _linear, _nonhomogeneous]]

13176

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

[[_2nd_order, _missing_x]]

13177

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

[[_2nd_order, _with_linear_symmetries]]

13183

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

[[_2nd_order, _missing_x]]

13188

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

[[_2nd_order, _linear, _nonhomogeneous]]

13190

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

[[_2nd_order, _missing_x]]

13193

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

[[_2nd_order, _missing_x]]

13196

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

[[_2nd_order, _missing_x]]

13318

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

[[_2nd_order, _with_linear_symmetries]]

13319

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

[[_2nd_order, _with_linear_symmetries]]

13321

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

[[_2nd_order, _missing_x]]

13322

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

[[_2nd_order, _missing_x]]

13325

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

[[_2nd_order, _missing_x]]

13334

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

[[_2nd_order, _with_linear_symmetries]]

13335

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x} \]

[[_2nd_order, _with_linear_symmetries]]

13336

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

[[_2nd_order, _missing_x]]

13337

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

[[_2nd_order, _missing_x]]

13338

\[ {}4 y^{\prime \prime }-12 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

13339

\[ {}3 y^{\prime \prime }-14 y^{\prime }-5 y = 0 \]

[[_2nd_order, _missing_x]]

13342

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

13343

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

[[_2nd_order, _missing_x]]

13344

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

[[_2nd_order, _missing_x]]

13345

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

13346

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

[[_2nd_order, _missing_x]]

13347

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

[[_2nd_order, _missing_x]]

13360

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

[[_2nd_order, _missing_x]]

13361

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

[[_2nd_order, _missing_x]]

13362

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13363

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

[[_2nd_order, _missing_x]]

13364

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

[[_2nd_order, _missing_x]]

13365

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

[[_2nd_order, _missing_x]]

13366

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

[[_2nd_order, _missing_x]]

13367

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

[[_2nd_order, _missing_x]]

13368

\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13369

\[ {}y^{\prime \prime }+6 y^{\prime }+58 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13370

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

[[_2nd_order, _missing_x]]

13371

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

[[_2nd_order, _missing_x]]

13372

\[ {}9 y^{\prime \prime }+6 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13373

\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13380

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

[[_2nd_order, _with_linear_symmetries]]

13381

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13382

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13383

\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13384

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

[[_2nd_order, _linear, _nonhomogeneous]]

13385

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

13386

\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13387

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

[[_2nd_order, _linear, _nonhomogeneous]]

13392

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \]

[[_2nd_order, _linear, _nonhomogeneous]]

13393

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

[[_2nd_order, _linear, _nonhomogeneous]]

13400

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

[[_2nd_order, _linear, _nonhomogeneous]]

13401

\[ {}y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13404

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13405

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13406

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 9 x \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13407

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13408

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13409

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13410

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13411

\[ {}y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

13412

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13413

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

13414

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

[[_2nd_order, _linear, _nonhomogeneous]]

13415

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

[[_2nd_order, _linear, _nonhomogeneous]]

13416

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

[[_2nd_order, _linear, _nonhomogeneous]]

13417

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

[[_2nd_order, _linear, _nonhomogeneous]]

13420

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13421

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

[[_2nd_order, _linear, _nonhomogeneous]]

13422

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

[[_2nd_order, _linear, _nonhomogeneous]]

13423

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13424

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

[[_2nd_order, _linear, _nonhomogeneous]]

13434

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

[[_2nd_order, _linear, _nonhomogeneous]]

13435

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

[[_2nd_order, _linear, _nonhomogeneous]]

13436

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

[[_2nd_order, _linear, _nonhomogeneous]]

13437

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

[[_2nd_order, _linear, _nonhomogeneous]]

13438

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

[[_2nd_order, _linear, _nonhomogeneous]]

13439

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

[[_2nd_order, _linear, _nonhomogeneous]]

13440

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

[[_2nd_order, _linear, _nonhomogeneous]]

13441

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

[[_2nd_order, _linear, _nonhomogeneous]]

13442

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

[[_2nd_order, _linear, _nonhomogeneous]]

13443

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

[[_2nd_order, _linear, _nonhomogeneous]]

13444

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

[[_2nd_order, _linear, _nonhomogeneous]]

13445

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

[[_2nd_order, _linear, _nonhomogeneous]]

13446

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

[[_2nd_order, _linear, _nonhomogeneous]]

13447

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

[[_2nd_order, _linear, _nonhomogeneous]]

13448

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

[[_2nd_order, _linear, _nonhomogeneous]]

13449

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

[[_2nd_order, _linear, _nonhomogeneous]]

13450

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

[[_2nd_order, _linear, _nonhomogeneous]]

13451

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

[[_2nd_order, _linear, _nonhomogeneous]]

13607

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

[[_2nd_order, _missing_x]]

13608

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

[[_2nd_order, _missing_x]]

13609

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

[[_2nd_order, _missing_x]]

13610

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

[[_2nd_order, _missing_x]]

13679

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

[[_2nd_order, _missing_x]]

13680

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

[[_2nd_order, _missing_x]]

13681

\[ {}z^{\prime \prime }-4 z^{\prime }+13 z = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13682

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

[[_2nd_order, _missing_x]]

13683

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

[[_2nd_order, _missing_x]]

13684

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

[[_2nd_order, _missing_x]]

13685

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

[[_2nd_order, _missing_x]]

13686

\[ {}2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13687

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

[[_2nd_order, _missing_x]]

13688

\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13689

\[ {}4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13690

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

[[_2nd_order, _missing_x]]

13691

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

[[_2nd_order, _missing_x]]

13692

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

[[_2nd_order, _missing_x]]

13693

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

[[_2nd_order, _missing_x]]

13694

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

[[_2nd_order, _with_linear_symmetries]]

13695

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

[[_2nd_order, _missing_y]]

13696

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

[[_2nd_order, _with_linear_symmetries]]

13697

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

[[_2nd_order, _with_linear_symmetries]]

13698

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

[[_2nd_order, _with_linear_symmetries]]

13699

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

[[_2nd_order, _linear, _nonhomogeneous]]

13700

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

[[_2nd_order, _linear, _nonhomogeneous]]

13701

\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

13702

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

[[_2nd_order, _linear, _nonhomogeneous]]

13703

\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13704

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

[[_2nd_order, _with_linear_symmetries]]

13705

\[ {}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13706

\[ {}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

13707

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

[[_2nd_order, _linear, _nonhomogeneous]]

13708

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

[[_2nd_order, _linear, _nonhomogeneous]]

13719

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

[[_2nd_order, _with_linear_symmetries]]

13720

\[ {}x^{\prime \prime }-x = \frac {1}{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

13721

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

[[_2nd_order, _linear, _nonhomogeneous]]

13723

\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \]

[[_2nd_order, _missing_y]]

13829

\[ {}y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]
i.c.

[[_2nd_order, _missing_x]]

13830

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

[[_2nd_order, _linear, _nonhomogeneous]]

13832

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

[[_2nd_order, _linear, _nonhomogeneous]]

13834

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

[[_2nd_order, _linear, _nonhomogeneous]]

13836

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

[[_2nd_order, _linear, _nonhomogeneous]]

13847

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

[[_2nd_order, _linear, _nonhomogeneous]]

13851

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

[[_2nd_order, _linear, _nonhomogeneous]]

13852

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

[[_2nd_order, _linear, _nonhomogeneous]]

13854

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

[[_2nd_order, _linear, _nonhomogeneous]]

13864

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

[[_2nd_order, _linear, _nonhomogeneous]]

13870

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

[[_2nd_order, _linear, _nonhomogeneous]]

13902

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

[[_2nd_order, _with_linear_symmetries]]

13909

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

[[_2nd_order, _missing_x]]

13911

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

[[_2nd_order, _missing_x]]

14021

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

[[_2nd_order, _missing_x]]

14022

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

[[_2nd_order, _with_linear_symmetries]]

14023

\[ {}y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]

[[_2nd_order, _missing_x]]

14025

\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

14061

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

[[_2nd_order, _linear, _nonhomogeneous]]

14062

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

[[_2nd_order, _linear, _nonhomogeneous]]

14064

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

[[_2nd_order, _linear, _nonhomogeneous]]

14078

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

[[_2nd_order, _missing_x]]

14079

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

[[_2nd_order, _missing_x]]

14088

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

[[_2nd_order, _with_linear_symmetries]]

14157

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

[[_2nd_order, _missing_x]]

14166

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

[[_2nd_order, _missing_x]]

14167

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

[[_2nd_order, _missing_x]]

14168

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

[[_2nd_order, _missing_x]]

14169

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

[[_2nd_order, _missing_x]]

14170

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

[[_2nd_order, _missing_x]]

14171

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

[[_2nd_order, _missing_x]]

14172

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

[[_2nd_order, _missing_x]]

14173

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

[[_2nd_order, _missing_x]]

14174

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

[[_2nd_order, _missing_x]]

14183

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

[[_2nd_order, _with_linear_symmetries]]

14184

\[ {}s^{\prime \prime }-a^{2} s = 1+t \]

[[_2nd_order, _with_linear_symmetries]]

14185

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

[[_2nd_order, _linear, _nonhomogeneous]]

14186

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

[[_2nd_order, _with_linear_symmetries]]

14187

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

[[_2nd_order, _with_linear_symmetries]]

14188

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

[[_2nd_order, _with_linear_symmetries]]

14189

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

[[_2nd_order, _with_linear_symmetries]]

14190

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

[[_2nd_order, _missing_y]]

14191

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

[[_2nd_order, _linear, _nonhomogeneous]]

14192

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

[[_2nd_order, _linear, _nonhomogeneous]]

14197

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

[[_2nd_order, _linear, _nonhomogeneous]]

14198

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14199

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

[[_2nd_order, _linear, _nonhomogeneous]]

14200

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

[[_2nd_order, _linear, _nonhomogeneous]]

14207

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

[[_2nd_order, _linear, _nonhomogeneous]]

14210

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

[[_2nd_order, _linear, _nonhomogeneous]]

14242

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

[[_2nd_order, _missing_x]]

14252

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

[[_2nd_order, _missing_x]]

14253

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

[[_2nd_order, _missing_x]]

14264

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

[[_2nd_order, _missing_x]]

14266

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

[[_2nd_order, _missing_x]]

14269

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

[[_2nd_order, _missing_x]]

14270

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

[[_2nd_order, _missing_x]]

14271

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

[[_2nd_order, _missing_x]]

14272

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

[[_2nd_order, _missing_x]]

14409

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

[[_2nd_order, _with_linear_symmetries]]

14415

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

[[_2nd_order, _missing_x]]

14416

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

[[_2nd_order, _missing_x]]

14419

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

[[_2nd_order, _missing_x]]

14422

\[ {}y^{\prime \prime }-4 y = 31 \]
i.c.

[[_2nd_order, _missing_x]]

14423

\[ {}y^{\prime \prime }+9 y = 27 x +18 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14425

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

[[_2nd_order, _missing_x]]

14435

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

[[_2nd_order, _missing_x]]

14791

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

[[_2nd_order, _missing_x]]

14792

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

[[_2nd_order, _missing_x]]

14822

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

[[_2nd_order, _missing_x]]

14823

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

[[_2nd_order, _missing_x]]

14824

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

[[_2nd_order, _missing_x]]

14825

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

[[_2nd_order, _missing_x]]

14826

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \]

[[_2nd_order, _with_linear_symmetries]]

14827

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \]

[[_2nd_order, _with_linear_symmetries]]

14828

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

[[_2nd_order, _with_linear_symmetries]]

14829

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

14830

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

14831

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

14832

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

[[_2nd_order, _with_linear_symmetries]]

14833

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

[[_2nd_order, _with_linear_symmetries]]

14834

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14835

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14836

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14837

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14838

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

[[_2nd_order, _with_linear_symmetries]]

14839

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

[[_2nd_order, _with_linear_symmetries]]

14840

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

[[_2nd_order, _with_linear_symmetries]]

14841

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14842

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14843

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14844

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

[[_2nd_order, _with_linear_symmetries]]

14845

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

[[_2nd_order, _missing_x]]

14846

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 2 \]
i.c.

[[_2nd_order, _missing_x]]

14847

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

[[_2nd_order, _missing_x]]

14848

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \]
i.c.

[[_2nd_order, _missing_x]]

14849

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

[[_2nd_order, _with_linear_symmetries]]

14850

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

[[_2nd_order, _with_linear_symmetries]]

14851

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

[[_2nd_order, _missing_x]]

14852

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

[[_2nd_order, _with_linear_symmetries]]

14853

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

[[_2nd_order, _missing_x]]

14854

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

[[_2nd_order, _with_linear_symmetries]]

14855

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

[[_2nd_order, _with_linear_symmetries]]

14856

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

[[_2nd_order, _missing_y]]

14857

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

[[_2nd_order, _missing_y]]

14858

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

[[_2nd_order, _with_linear_symmetries]]

14859

\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14860

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14861

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

[[_2nd_order, _with_linear_symmetries]]

14862

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14863

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

14864

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

[[_2nd_order, _with_linear_symmetries]]

14865

\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14866

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

[[_2nd_order, _linear, _nonhomogeneous]]

14867

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

[[_2nd_order, _linear, _nonhomogeneous]]

14868

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

[[_2nd_order, _linear, _nonhomogeneous]]

14869

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

[[_2nd_order, _linear, _nonhomogeneous]]

14870

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14871

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14872

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14873

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14874

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14875

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

[[_2nd_order, _linear, _nonhomogeneous]]

14876

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

[[_2nd_order, _linear, _nonhomogeneous]]

14877

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14878

\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

14879

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

[[_2nd_order, _linear, _nonhomogeneous]]

14880

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

[[_2nd_order, _linear, _nonhomogeneous]]

14881

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14882

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14883

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

[[_2nd_order, _linear, _nonhomogeneous]]

14884

\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

14885

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

[[_2nd_order, _linear, _nonhomogeneous]]

14886

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

[[_2nd_order, _linear, _nonhomogeneous]]

14887

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

[[_2nd_order, _linear, _nonhomogeneous]]

14913

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

[[_2nd_order, _quadrature]]

14916

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

[[_2nd_order, _linear, _nonhomogeneous]]

14927

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

[[_2nd_order, _quadrature]]

14928

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

[[_2nd_order, _quadrature]]

15140

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

[[_2nd_order, _missing_x]]

15141

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

[[_2nd_order, _missing_y]]

15150

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

[[_2nd_order, _missing_x]]

15152

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

[[_2nd_order, _missing_y]]

15160

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

[[_2nd_order, _missing_x]]

15170

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

[[_2nd_order, _missing_y]]

15174

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

[[_2nd_order, _missing_x]]

15175

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

[[_2nd_order, _missing_y]]

15198

\[ {}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15225

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

[[_2nd_order, _missing_x]]

15226

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

[[_2nd_order, _missing_x]]

15227

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

[[_2nd_order, _missing_x]]

15228

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

[[_2nd_order, _missing_x]]

15238

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

[[_2nd_order, _missing_x]]

15239

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

[[_2nd_order, _missing_x]]

15240

\[ {}y^{\prime \prime }-10 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15241

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

[[_2nd_order, _missing_x]]

15244

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

[[_2nd_order, _missing_x]]

15245

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 0 \]

[[_2nd_order, _missing_x]]

15246

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

[[_2nd_order, _missing_x]]

15247

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

[[_2nd_order, _missing_x]]

15248

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

[[_2nd_order, _missing_x]]

15249

\[ {}3 y^{\prime \prime }+7 y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

15250

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15251

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15252

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15253

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

[[_2nd_order, _missing_x]]

15254

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

[[_2nd_order, _missing_x]]

15255

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

[[_2nd_order, _missing_x]]

15256

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

[[_2nd_order, _missing_x]]

15257

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

[[_2nd_order, _missing_x]]

15258

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

[[_2nd_order, _missing_x]]

15259

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

[[_2nd_order, _missing_x]]

15260

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

[[_2nd_order, _missing_x]]

15261

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

[[_2nd_order, _missing_x]]

15262

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

[[_2nd_order, _missing_x]]

15263

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

[[_2nd_order, _missing_x]]

15264

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

[[_2nd_order, _missing_x]]

15265

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

[[_2nd_order, _missing_x]]

15266

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

[[_2nd_order, _missing_x]]

15267

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

[[_2nd_order, _missing_x]]

15268

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

[[_2nd_order, _missing_x]]

15269

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

[[_2nd_order, _missing_x]]

15270

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

[[_2nd_order, _missing_x]]

15271

\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \]

[[_2nd_order, _missing_x]]

15272

\[ {}9 y^{\prime \prime }+18 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

15273

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

[[_2nd_order, _missing_x]]

15274

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

[[_2nd_order, _missing_x]]

15275

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

[[_2nd_order, _missing_x]]

15276

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

[[_2nd_order, _missing_x]]

15277

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

[[_2nd_order, _missing_x]]

15278

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

[[_2nd_order, _missing_x]]

15279

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

[[_2nd_order, _missing_x]]

15280

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

[[_2nd_order, _missing_x]]

15281

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

[[_2nd_order, _missing_x]]

15340

\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15341

\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15342

\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15343

\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15344

\[ {}y^{\prime \prime }-9 y = 36 \]
i.c.

[[_2nd_order, _missing_x]]

15345

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -6 \,{\mathrm e}^{4 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15346

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{5 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15347

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 169 \sin \left (2 x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15350

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

15351

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

15352

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15353

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15361

\[ {}y^{\prime \prime }+9 y = 52 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

15362

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x} \]

[[_2nd_order, _with_linear_symmetries]]

15363

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x} \]

[[_2nd_order, _with_linear_symmetries]]

15364

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

[[_2nd_order, _missing_y]]

15365

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15366

\[ {}y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15367

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15368

\[ {}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \]

[[_2nd_order, _missing_y]]

15369

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

[[_2nd_order, _linear, _nonhomogeneous]]

15370

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15371

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -200 \]

[[_2nd_order, _missing_x]]

15372

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

[[_2nd_order, _linear, _nonhomogeneous]]

15373

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4 \]

[[_2nd_order, _with_linear_symmetries]]

15374

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

[[_2nd_order, _linear, _nonhomogeneous]]

15375

\[ {}y^{\prime \prime }+9 y = x^{3} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15376

\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15377

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15378

\[ {}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15379

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

[[_2nd_order, _quadrature]]

15380

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15381

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15382

\[ {}y^{\prime \prime }+9 y = 39 x \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

15383

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

15384

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

[[_2nd_order, _missing_x]]

15385

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

[[_2nd_order, _missing_y]]

15386

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

[[_2nd_order, _linear, _nonhomogeneous]]

15387

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15388

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15389

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15390

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

15391

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x} \]

[[_2nd_order, _with_linear_symmetries]]

15392

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15393

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15394

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

[[_2nd_order, _linear, _nonhomogeneous]]

15395

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

[[_2nd_order, _linear, _nonhomogeneous]]

15396

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 100 \]

[[_2nd_order, _missing_x]]

15397

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

[[_2nd_order, _with_linear_symmetries]]

15398

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8 \]

[[_2nd_order, _with_linear_symmetries]]

15399

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

[[_2nd_order, _linear, _nonhomogeneous]]

15400

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

[[_2nd_order, _linear, _nonhomogeneous]]

15401

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

[[_2nd_order, _linear, _nonhomogeneous]]

15402

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

[[_2nd_order, _linear, _nonhomogeneous]]

15403

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

[[_2nd_order, _linear, _nonhomogeneous]]

15404

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15405

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

[[_2nd_order, _with_linear_symmetries]]

15406

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x} \]

[[_2nd_order, _with_linear_symmetries]]

15407

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15408

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15409

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

[[_2nd_order, _linear, _nonhomogeneous]]

15410

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15411

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15412

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15413

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15414

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15415

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15430

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15431

\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15432

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

[[_2nd_order, _linear, _nonhomogeneous]]

15433

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15443

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

[[_2nd_order, _linear, _nonhomogeneous]]

15444

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

[[_2nd_order, _linear, _nonhomogeneous]]

15445

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15446

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15447

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

[[_2nd_order, _linear, _nonhomogeneous]]

15457

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15464

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

[[_2nd_order, _missing_x]]

15465

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

[[_2nd_order, _missing_x]]

15467

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

[[_2nd_order, _missing_x]]

15468

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 0 \]

[[_2nd_order, _missing_x]]

15472

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

[[_2nd_order, _missing_x]]

15473

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

[[_2nd_order, _missing_x]]

15478

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

[[_2nd_order, _missing_x]]

15481

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

[[_2nd_order, _missing_x]]

15483

\[ {}y^{\prime \prime }+y^{\prime }-30 y = 0 \]

[[_2nd_order, _missing_x]]

15484

\[ {}16 y^{\prime \prime }-8 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

15490

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

[[_2nd_order, _missing_x]]

15491

\[ {}y^{\prime \prime }+20 y^{\prime }+100 y = 0 \]

[[_2nd_order, _missing_x]]

15493

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

[[_2nd_order, _missing_x]]

15494

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

15495

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15496

\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15497

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15499

\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15500

\[ {}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15502

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x} \]

[[_2nd_order, _with_linear_symmetries]]

15504

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15508

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

15509

\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

15710

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

[[_2nd_order, _linear, _nonhomogeneous]]

15722

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

[[_2nd_order, _missing_x]]

15723

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

[[_2nd_order, _missing_x]]

15724

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

[[_2nd_order, _missing_x]]

15725

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

[[_2nd_order, _linear, _nonhomogeneous]]

15726

\[ {}y^{\prime \prime }-12 y^{\prime }+40 y = 0 \]

[[_2nd_order, _missing_x]]

15751

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

[[_2nd_order, _missing_x]]

15752

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

[[_2nd_order, _missing_x]]

15764

\[ {}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0 \]

[[_2nd_order, _missing_x]]

15773

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

[[_2nd_order, _missing_x]]

15774

\[ {}y^{\prime \prime }-6 y^{\prime }+45 y = 0 \]

[[_2nd_order, _missing_x]]

15777

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

[[_2nd_order, _with_linear_symmetries]]

15778

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 2 \]

[[_2nd_order, _missing_x]]

15786

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

[[_2nd_order, _with_linear_symmetries]]

16106

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

[[_2nd_order, _missing_x]]

16107

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

[[_2nd_order, _missing_x]]

16109

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

[[_2nd_order, _missing_x]]

16110

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

[[_2nd_order, _missing_x]]

16111

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

[[_2nd_order, _missing_x]]

16114

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

[[_2nd_order, _linear, _nonhomogeneous]]

16115

\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 0 \]

[[_2nd_order, _missing_x]]

16116

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

[[_2nd_order, _missing_x]]

16117

\[ {}y^{\prime \prime }+6 y^{\prime }+18 y = 0 \]

[[_2nd_order, _missing_x]]

16135

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

[[_2nd_order, _quadrature]]

16136

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

[[_2nd_order, _missing_x]]

16137

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

[[_2nd_order, _missing_x]]

16138

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

[[_2nd_order, _missing_x]]

16139

\[ {}y^{\prime \prime }+8 y^{\prime }+12 y = 0 \]

[[_2nd_order, _missing_x]]

16140

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

[[_2nd_order, _missing_x]]

16141

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16142

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

[[_2nd_order, _missing_x]]

16143

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

[[_2nd_order, _missing_x]]

16144

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

[[_2nd_order, _missing_x]]

16145

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

[[_2nd_order, _missing_x]]

16146

\[ {}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

16147

\[ {}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

16148

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

[[_2nd_order, _missing_x]]

16149

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

[[_2nd_order, _missing_x]]

16150

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

[[_2nd_order, _missing_x]]

16151

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

[[_2nd_order, _missing_x]]

16152

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

[[_2nd_order, _missing_x]]

16153

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16154

\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16155

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

[[_2nd_order, _missing_x]]

16156

\[ {}y^{\prime \prime }+36 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16157

\[ {}y^{\prime \prime }+100 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16158

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

[[_2nd_order, _missing_x]]

16159

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

[[_2nd_order, _missing_x]]

16160

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

[[_2nd_order, _missing_x]]

16161

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

[[_2nd_order, _missing_x]]

16162

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

[[_2nd_order, _missing_x]]

16163

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

[[_2nd_order, _missing_x]]

16164

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

[[_2nd_order, _missing_x]]

16165

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

[[_2nd_order, _missing_x]]

16166

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

[[_2nd_order, _missing_x]]

16167

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

[[_2nd_order, _missing_x]]

16168

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

[[_2nd_order, _missing_x]]

16172

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

[[_2nd_order, _missing_x]]

16173

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

[[_2nd_order, _missing_x]]

16174

\[ {}y^{\prime \prime }-6 y^{\prime }-16 y = 0 \]

[[_2nd_order, _missing_x]]

16175

\[ {}y^{\prime \prime }-16 y = 0 \]

[[_2nd_order, _missing_x]]

16176

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

[[_2nd_order, _missing_x]]

16179

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

[[_2nd_order, _missing_x]]

16180

\[ {}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t} \]

[[_2nd_order, _with_linear_symmetries]]

16181

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

[[_2nd_order, _with_linear_symmetries]]

16182

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

[[_2nd_order, _with_linear_symmetries]]

16183

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

[[_2nd_order, _with_linear_symmetries]]

16184

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

[[_2nd_order, _with_linear_symmetries]]

16185

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

[[_2nd_order, _missing_y]]

16186

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

[[_2nd_order, _linear, _nonhomogeneous]]

16187

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

[[_2nd_order, _linear, _nonhomogeneous]]

16188

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

[[_2nd_order, _linear, _nonhomogeneous]]

16189

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

[[_2nd_order, _linear, _nonhomogeneous]]

16190

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

[[_2nd_order, _quadrature]]

16191

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

[[_2nd_order, _linear, _nonhomogeneous]]

16192

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

[[_2nd_order, _missing_x]]

16193

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

[[_2nd_order, _missing_x]]

16194

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t \]

[[_2nd_order, _with_linear_symmetries]]

16195

\[ {}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t \]

[[_2nd_order, _with_linear_symmetries]]

16196

\[ {}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t \]

[[_2nd_order, _with_linear_symmetries]]

16197

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

16198

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

16199

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16200

\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \]

[[_2nd_order, _missing_y]]

16201

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16202

\[ {}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16203

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16204

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16205

\[ {}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

16206

\[ {}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16207

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16208

\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

16209

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

[[_2nd_order, _missing_y]]

16210

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

16211

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

[[_2nd_order, _missing_y]]

16212

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

[[_2nd_order, _quadrature]]

16213

\[ {}y^{\prime \prime }+3 y^{\prime } = 18 \]
i.c.

[[_2nd_order, _missing_x]]

16214

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

[[_2nd_order, _missing_x]]

16215

\[ {}y^{\prime \prime }-4 y = 32 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

16216

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

[[_2nd_order, _missing_x]]

16217

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

[[_2nd_order, _with_linear_symmetries]]

16218

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 4 \]
i.c.

[[_2nd_order, _missing_x]]

16219

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16220

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = -1 \]
i.c.

[[_2nd_order, _missing_x]]

16221

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

[[_2nd_order, _missing_y]]

16222

\[ {}y^{\prime \prime }-y^{\prime } = -3 t -4 \,{\mathrm e}^{2 t} t^{2} \]
i.c.

[[_2nd_order, _missing_y]]

16223

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

[[_2nd_order, _missing_y]]

16224

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _missing_y]]

16225

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

[[_2nd_order, _missing_y]]

16226

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16227

\[ {}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16228

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16234

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

[[_2nd_order, _linear, _nonhomogeneous]]

16235

\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16236

\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16237

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

[[_2nd_order, _missing_x]]

16238

\[ {}y^{\prime \prime }+16 y^{\prime } = t \]

[[_2nd_order, _missing_y]]

16239

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t} \]

[[_2nd_order, _with_linear_symmetries]]

16240

\[ {}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16241

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16242

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

[[_2nd_order, _linear, _nonhomogeneous]]

16243

\[ {}y^{\prime \prime }+16 y = \csc \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16244

\[ {}y^{\prime \prime }+16 y = \cot \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16245

\[ {}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16246

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16247

\[ {}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16248

\[ {}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16249

\[ {}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16250

\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16251

\[ {}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16252

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16253

\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16254

\[ {}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16255

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

[[_2nd_order, _linear, _nonhomogeneous]]

16256

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

[[_2nd_order, _linear, _nonhomogeneous]]

16257

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

[[_2nd_order, _linear, _nonhomogeneous]]

16258

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16259

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

[[_2nd_order, _linear, _nonhomogeneous]]

16260

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

[[_2nd_order, _linear, _nonhomogeneous]]

16261

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

[[_2nd_order, _linear, _nonhomogeneous]]

16262

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16263

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

[[_2nd_order, _linear, _nonhomogeneous]]

16264

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16265

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

[[_2nd_order, _linear, _nonhomogeneous]]

16266

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16267

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

[[_2nd_order, _linear, _nonhomogeneous]]

16268

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

[[_2nd_order, _linear, _nonhomogeneous]]

16269

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

[[_2nd_order, _linear, _nonhomogeneous]]

16270

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

[[_2nd_order, _linear, _nonhomogeneous]]

16271

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

[[_2nd_order, _linear, _nonhomogeneous]]

16272

\[ {}y^{\prime \prime }+16 y = \tan \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16273

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

[[_2nd_order, _linear, _nonhomogeneous]]

16274

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

[[_2nd_order, _linear, _nonhomogeneous]]

16275

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

[[_2nd_order, _linear, _nonhomogeneous]]

16276

\[ {}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16277

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

[[_2nd_order, _linear, _nonhomogeneous]]

16278

\[ {}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16279

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

[[_2nd_order, _linear, _nonhomogeneous]]

16280

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16281

\[ {}y^{\prime \prime }+9 y = \csc \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16282

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16286

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

[[_2nd_order, _with_linear_symmetries]]

16287

\[ {}y^{\prime \prime }+4 y = f \left (t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16487

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

[[_2nd_order, _missing_x]]

16488

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

[[_2nd_order, _missing_x]]

16489

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

[[_2nd_order, _missing_x]]

16492

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

[[_2nd_order, _missing_x]]

16493

\[ {}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

16494

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

[[_2nd_order, _missing_x]]

16495

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

[[_2nd_order, _missing_x]]

16496

\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = 0 \]

[[_2nd_order, _missing_x]]

16497

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

[[_2nd_order, _missing_x]]

16498

\[ {}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

16499

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

[[_2nd_order, _missing_x]]

16500

\[ {}12 y^{\prime \prime }+8 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16504

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

[[_2nd_order, _with_linear_symmetries]]

16505

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

[[_2nd_order, _missing_y]]

16506

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

[[_2nd_order, _missing_y]]

16507

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

[[_2nd_order, _linear, _nonhomogeneous]]

16508

\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16509

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

[[_2nd_order, _missing_y]]

16510

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

[[_2nd_order, _with_linear_symmetries]]

16511

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _with_linear_symmetries]]

16512

\[ {}y^{\prime \prime }+9 y^{\prime }+20 y = -2 \,{\mathrm e}^{t} t \]

[[_2nd_order, _linear, _nonhomogeneous]]

16513

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16518

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

[[_2nd_order, _missing_x]]

16519

\[ {}y^{\prime \prime }+10 y^{\prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16520

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

[[_2nd_order, _missing_x]]

16521

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

[[_2nd_order, _missing_x]]

16522

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

[[_2nd_order, _with_linear_symmetries]]

16523

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

[[_2nd_order, _with_linear_symmetries]]

16524

\[ {}y^{\prime \prime }+9 y = \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16525

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

[[_2nd_order, _linear, _nonhomogeneous]]

16526

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

[[_2nd_order, _linear, _nonhomogeneous]]

16527

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

[[_2nd_order, _linear, _nonhomogeneous]]

16528

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16529

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16530

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

[[_2nd_order, _linear, _nonhomogeneous]]

16531

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

[[_2nd_order, _linear, _nonhomogeneous]]

16533

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

[[_2nd_order, _missing_x]]

16534

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

[[_2nd_order, _missing_x]]

16552

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

[[_2nd_order, _missing_x]]

16553

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

[[_2nd_order, _missing_x]]

16554

\[ {}x^{\prime \prime }+64 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16555

\[ {}x^{\prime \prime }+100 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16556

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

[[_2nd_order, _missing_x]]

16557

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

[[_2nd_order, _missing_x]]

16558

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

[[_2nd_order, _missing_x]]

16559

\[ {}x^{\prime \prime }+256 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16560

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

[[_2nd_order, _missing_x]]

16561

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

[[_2nd_order, _missing_x]]

16562

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

[[_2nd_order, _missing_x]]

16563

\[ {}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16564

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

[[_2nd_order, _missing_x]]

16565

\[ {}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16566

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16567

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

[[_2nd_order, _missing_x]]

16568

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16570

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16571

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16572

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

[[_2nd_order, _linear, _nonhomogeneous]]

16573

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

[[_2nd_order, _linear, _nonhomogeneous]]

16574

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

[[_2nd_order, _linear, _nonhomogeneous]]

16575

\[ {}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16576

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

16589

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

[[_2nd_order, _missing_x]]

16590

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

[[_2nd_order, _missing_x]]

16591

\[ {}x^{\prime \prime }+16 x = t \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16592

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

[[_2nd_order, _with_linear_symmetries]]

16835

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

[[_2nd_order, _linear, _nonhomogeneous]]

16840

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

[[_2nd_order, _missing_x]]

16841

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

[[_2nd_order, _missing_x]]

16847

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

[[_2nd_order, _quadrature]]

16848

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

[[_2nd_order, _quadrature]]

16864

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

[[_2nd_order, _missing_x]]

16881

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

[[_2nd_order, _missing_x]]

16882

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

[[_2nd_order, _missing_x]]

16884

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

[[_2nd_order, _missing_x]]

16885

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

[[_2nd_order, _missing_x]]

16887

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

[[_2nd_order, _missing_x]]

16889

\[ {}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

16892

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

[[_2nd_order, _missing_x]]

16893

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

[[_2nd_order, _missing_x]]

16903

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

[[_2nd_order, _missing_x]]

16904

\[ {}y^{\prime \prime }-7 y^{\prime } = \left (x -1\right )^{2} \]

[[_2nd_order, _missing_y]]

16905

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

[[_2nd_order, _missing_y]]

16906

\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \]

[[_2nd_order, _missing_y]]

16907

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16908

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

[[_2nd_order, _with_linear_symmetries]]

16909

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

[[_2nd_order, _missing_y]]

16910

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

[[_2nd_order, _missing_y]]

16911

\[ {}y^{\prime \prime }+25 y = \cos \left (5 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16912

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

[[_2nd_order, _linear, _nonhomogeneous]]

16913

\[ {}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16914

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

[[_2nd_order, _linear, _nonhomogeneous]]

16915

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

[[_2nd_order, _linear, _nonhomogeneous]]

16916

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

[[_2nd_order, _linear, _nonhomogeneous]]

16917

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

[[_2nd_order, _linear, _nonhomogeneous]]

16918

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

[[_2nd_order, _missing_x]]

16939

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

[[_2nd_order, _missing_x]]

16940

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

[[_2nd_order, _missing_x]]

16941

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

[[_2nd_order, _missing_x]]

16947

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

[[_2nd_order, _with_linear_symmetries]]

16948

\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \]

[[_2nd_order, _missing_y]]

16949

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

[[_2nd_order, _with_linear_symmetries]]

16950

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

[[_2nd_order, _with_linear_symmetries]]

16951

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

[[_2nd_order, _with_linear_symmetries]]

16952

\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \]

[[_2nd_order, _missing_y]]

16953

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

[[_2nd_order, _missing_y]]

16954

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

16955

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

[[_2nd_order, _with_linear_symmetries]]

16956

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

[[_2nd_order, _linear, _nonhomogeneous]]

16957

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

[[_2nd_order, _linear, _nonhomogeneous]]

16958

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

[[_2nd_order, _linear, _nonhomogeneous]]

16959

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

[[_2nd_order, _linear, _nonhomogeneous]]

16960

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

[[_2nd_order, _linear, _nonhomogeneous]]

16961

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

[[_2nd_order, _linear, _nonhomogeneous]]

16962

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

[[_2nd_order, _missing_y]]

16963

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

[[_2nd_order, _missing_y]]

16964

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16965

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

[[_2nd_order, _missing_y]]

16966

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

[[_2nd_order, _linear, _nonhomogeneous]]

16967

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

[[_2nd_order, _linear, _nonhomogeneous]]

16968

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

[[_2nd_order, _linear, _nonhomogeneous]]

16971

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

[[_2nd_order, _linear, _nonhomogeneous]]

16973

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

[[_2nd_order, _linear, _nonhomogeneous]]

16974

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

[[_2nd_order, _linear, _nonhomogeneous]]

16978

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

[[_2nd_order, _linear, _nonhomogeneous]]

16979

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

[[_2nd_order, _linear, _nonhomogeneous]]

16980

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

[[_2nd_order, _missing_y]]

16981

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

[[_2nd_order, _linear, _nonhomogeneous]]

16982

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

[[_2nd_order, _linear, _nonhomogeneous]]

16985

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

[[_2nd_order, _linear, _nonhomogeneous]]

16986

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

[[_2nd_order, _missing_y]]

16987

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

[[_2nd_order, _with_linear_symmetries]]

16988

\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \]

[[_2nd_order, _missing_y]]

16989

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

[[_2nd_order, _linear, _nonhomogeneous]]

16990

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

[[_2nd_order, _linear, _nonhomogeneous]]

16991

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16992

\[ {}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16993

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

[[_2nd_order, _linear, _nonhomogeneous]]

16995

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

[[_2nd_order, _missing_y]]

16997

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

16998

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

[[_2nd_order, _missing_y]]

16999

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

[[_2nd_order, _linear, _nonhomogeneous]]

17000

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

[[_2nd_order, _linear, _nonhomogeneous]]

17001

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

[[_2nd_order, _linear, _nonhomogeneous]]

17002

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

[[_2nd_order, _linear, _nonhomogeneous]]

17003

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17004

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

[[_2nd_order, _linear, _nonhomogeneous]]

17005

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

[[_2nd_order, _missing_y]]

17006

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

17007

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

[[_2nd_order, _linear, _nonhomogeneous]]

17008

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

[[_2nd_order, _linear, _nonhomogeneous]]

17009

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

[[_2nd_order, _linear, _nonhomogeneous]]

17010

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17011

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

[[_2nd_order, _missing_y]]

17013

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

[[_2nd_order, _linear, _nonhomogeneous]]

17018

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

[[_2nd_order, _with_linear_symmetries]]

17019

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17020

\[ {}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17021

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

[[_2nd_order, _with_linear_symmetries]]

17022

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17023

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

[[_2nd_order, _missing_y]]

17024

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17025

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

[[_2nd_order, _linear, _nonhomogeneous]]

17026

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

[[_2nd_order, _linear, _nonhomogeneous]]

17027

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

[[_2nd_order, _linear, _nonhomogeneous]]

17028

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

[[_2nd_order, _linear, _nonhomogeneous]]

17029

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

17030

\[ {}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \]
i.c.

[[_2nd_order, _missing_y]]

17031

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

[[_2nd_order, _linear, _nonhomogeneous]]

17036

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

[[_2nd_order, _linear, _nonhomogeneous]]

17037

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

[[_2nd_order, _linear, _nonhomogeneous]]

17038

\[ {}y^{\prime \prime }-y = 1 \]

[[_2nd_order, _missing_x]]

17039

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

[[_2nd_order, _linear, _nonhomogeneous]]

17042

\[ {}y^{\prime \prime }-y^{\prime }-5 y = 1 \]
i.c.

[[_2nd_order, _missing_x]]

17044

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17077

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

[[_2nd_order, _linear, _nonhomogeneous]]

17078

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

[[_2nd_order, _missing_y]]

17079

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

[[_2nd_order, _linear, _nonhomogeneous]]

17080

\[ {}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17081

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

[[_2nd_order, _linear, _nonhomogeneous]]

17082

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

[[_2nd_order, _linear, _nonhomogeneous]]

17083

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

[[_2nd_order, _linear, _nonhomogeneous]]

17084

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

[[_2nd_order, _missing_y]]

17099

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

[[_2nd_order, _missing_x]]

17100

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

[[_2nd_order, _missing_x]]

17101

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

[[_2nd_order, _missing_x]]

17109

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

[[_2nd_order, _missing_x]]

17110

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

[[_2nd_order, _missing_x]]

17111

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

[[_2nd_order, _missing_x]]

17114

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

[[_2nd_order, _missing_x]]

17115

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

[[_2nd_order, _missing_x]]

17116

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

[[_2nd_order, _missing_x]]

17117

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

[[_2nd_order, _missing_x]]

17118

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

[[_2nd_order, _missing_x]]

17119

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

[[_2nd_order, _missing_x]]

17120

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

[[_2nd_order, _missing_x]]

17121

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

[[_2nd_order, _missing_x]]

17153

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

[[_2nd_order, _linear, _nonhomogeneous]]

17154

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

[[_2nd_order, _with_linear_symmetries]]

17155

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

[[_2nd_order, _linear, _nonhomogeneous]]

17156

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

[[_2nd_order, _linear, _nonhomogeneous]]

17157

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

[[_2nd_order, _linear, _nonhomogeneous]]

17481

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

[[_2nd_order, _missing_x]]

17482

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

[[_2nd_order, _missing_x]]

17483

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

[[_2nd_order, _missing_x]]

17484

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

[[_2nd_order, _missing_x]]

17485

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

[[_2nd_order, _missing_x]]

17496

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

[[_2nd_order, _missing_x]]

17497

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

[[_2nd_order, _missing_x]]

17500

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

[[_2nd_order, _missing_x]]

17512

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

[[_2nd_order, _missing_x]]

17513

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

[[_2nd_order, _missing_x]]

17514

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

[[_2nd_order, _missing_x]]

17515

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

[[_2nd_order, _missing_x]]

17516

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

[[_2nd_order, _missing_x]]

17517

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

[[_2nd_order, _missing_x]]

17518

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

[[_2nd_order, _missing_x]]

17519

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

[[_2nd_order, _missing_x]]

17520

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

[[_2nd_order, _missing_x]]

17521

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

[[_2nd_order, _missing_x]]

17522

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

[[_2nd_order, _missing_x]]

17523

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

[[_2nd_order, _missing_x]]

17524

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

[[_2nd_order, _missing_x]]

17525

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

[[_2nd_order, _missing_x]]

17526

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

[[_2nd_order, _missing_x]]

17527

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

[[_2nd_order, _missing_x]]

17528

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

[[_2nd_order, _missing_x]]

17529

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

[[_2nd_order, _missing_x]]

17530

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

[[_2nd_order, _missing_x]]

17531

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

[[_2nd_order, _missing_x]]

17532

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

[[_2nd_order, _missing_x]]

17533

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

[[_2nd_order, _missing_x]]

17534

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

[[_2nd_order, _missing_x]]

17535

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

[[_2nd_order, _missing_x]]

17536

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

[[_2nd_order, _missing_x]]

17537

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

[[_2nd_order, _missing_x]]

17538

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

[[_2nd_order, _missing_x]]

17539

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

[[_2nd_order, _missing_x]]

17540

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

[[_2nd_order, _missing_x]]

17541

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

[[_2nd_order, _missing_x]]

17542

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

[[_2nd_order, _missing_x]]

17543

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

[[_2nd_order, _missing_x]]

17544

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

[[_2nd_order, _missing_x]]

17545

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

[[_2nd_order, _missing_x]]

17546

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

[[_2nd_order, _missing_x]]

17547

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

[[_2nd_order, _missing_x]]

17548

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

[[_2nd_order, _missing_x]]

17549

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

[[_2nd_order, _missing_x]]

17550

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

[[_2nd_order, _missing_x]]

17551

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

[[_2nd_order, _missing_x]]

17552

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

[[_2nd_order, _missing_x]]

17553

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

[[_2nd_order, _missing_x]]

17554

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

[[_2nd_order, _missing_x]]

17568

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

[[_2nd_order, _missing_x]]

17569

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

[[_2nd_order, _missing_x]]

17570

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

[[_2nd_order, _missing_x]]

17571

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

[[_2nd_order, _with_linear_symmetries]]

17572

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

[[_2nd_order, _linear, _nonhomogeneous]]

17573

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

[[_2nd_order, _linear, _nonhomogeneous]]

17574

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

[[_2nd_order, _missing_y]]

17575

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

[[_2nd_order, _linear, _nonhomogeneous]]

17576

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

[[_2nd_order, _with_linear_symmetries]]

17577

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

[[_2nd_order, _with_linear_symmetries]]

17578

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

[[_2nd_order, _with_linear_symmetries]]

17579

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

[[_2nd_order, _with_linear_symmetries]]

17580

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

[[_2nd_order, _with_linear_symmetries]]

17581

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

[[_2nd_order, _linear, _nonhomogeneous]]

17582

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

[[_2nd_order, _linear, _nonhomogeneous]]

17583

\[ {}u^{\prime \prime }+w_{0}^{2} u = \cos \left (w t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17584

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

[[_2nd_order, _linear, _nonhomogeneous]]

17585

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

[[_2nd_order, _linear, _nonhomogeneous]]

17586

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

[[_2nd_order, _with_linear_symmetries]]

17587

\[ {}y^{\prime \prime }+4 y = t^{2}+3 \,{\mathrm e}^{t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17588

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

[[_2nd_order, _linear, _nonhomogeneous]]

17589

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

[[_2nd_order, _linear, _nonhomogeneous]]

17590

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

[[_2nd_order, _linear, _nonhomogeneous]]

17591

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

[[_2nd_order, _linear, _nonhomogeneous]]

17592

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

[[_2nd_order, _missing_y]]

17593

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

[[_2nd_order, _linear, _nonhomogeneous]]

17594

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17595

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

[[_2nd_order, _linear, _nonhomogeneous]]

17596

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

[[_2nd_order, _linear, _nonhomogeneous]]

17597

\[ {}y^{\prime \prime }+4 y = t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17598

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

[[_2nd_order, _linear, _nonhomogeneous]]

17599

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 t \,{\mathrm e}^{-t} \cos \left (2 t \right )-2 t \,{\mathrm e}^{-2 t} \cos \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17600

\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 2 \,{\mathrm e}^{-t} \]

[[_2nd_order, _with_linear_symmetries]]

17605

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17606

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17607

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17608

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

[[_2nd_order, _linear, _nonhomogeneous]]

17609

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

[[_2nd_order, _linear, _nonhomogeneous]]

17610

\[ {}y^{\prime \prime }+y = 3 \cos \left (w t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

17611

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

[[_2nd_order, _linear, _nonhomogeneous]]

17612

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

[[_2nd_order, _linear, _nonhomogeneous]]

17613

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

[[_2nd_order, _linear, _nonhomogeneous]]

17616

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

[[_2nd_order, _with_linear_symmetries]]

17617

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

[[_2nd_order, _with_linear_symmetries]]

17618

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

[[_2nd_order, _with_linear_symmetries]]

17619

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

[[_2nd_order, _with_linear_symmetries]]

17620

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

[[_2nd_order, _linear, _nonhomogeneous]]

17621

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

[[_2nd_order, _linear, _nonhomogeneous]]

17622

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

[[_2nd_order, _linear, _nonhomogeneous]]

17623

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

[[_2nd_order, _linear, _nonhomogeneous]]

17624

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

[[_2nd_order, _linear, _nonhomogeneous]]

17625

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

[[_2nd_order, _linear, _nonhomogeneous]]

17626

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

[[_2nd_order, _linear, _nonhomogeneous]]

17627

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

[[_2nd_order, _linear, _nonhomogeneous]]

17638

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

[[_2nd_order, _linear, _nonhomogeneous]]

17822

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

[[_2nd_order, _quadrature]]

17934

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

[[_2nd_order, _missing_x]]

17943

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

[[_2nd_order, _missing_x]]

17945

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

[[_2nd_order, _with_linear_symmetries]]

17946

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

17949

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

[[_2nd_order, _linear, _nonhomogeneous]]

17950

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

[[_2nd_order, _linear, _nonhomogeneous]]

17951

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

[[_2nd_order, _linear, _nonhomogeneous]]

17952

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

[[_2nd_order, _linear, _nonhomogeneous]]

17953

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

[[_2nd_order, _linear, _nonhomogeneous]]

17954

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

[[_2nd_order, _linear, _nonhomogeneous]]

17989

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

[[_2nd_order, _missing_x]]

17990

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

[[_2nd_order, _missing_x]]

18030

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

[[_2nd_order, _missing_x]]

18118

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

[[_2nd_order, _missing_x]]

18180

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

[[_2nd_order, _with_linear_symmetries]]

18182

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

[[_2nd_order, _missing_x]]

18183

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

[[_2nd_order, _linear, _nonhomogeneous]]

18184

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

[[_2nd_order, _quadrature]]

18185

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

[[_2nd_order, _missing_x]]

18186

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

[[_2nd_order, _linear, _nonhomogeneous]]

18188

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

[[_2nd_order, _missing_y]]

18191

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

[[_2nd_order, _missing_x]]

18193

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

[[_2nd_order, _missing_x]]

18194

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

[[_2nd_order, _missing_x]]

18196

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

[[_2nd_order, _missing_x]]

18197

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

[[_2nd_order, _missing_x]]

18198

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

[[_2nd_order, _missing_x]]

18217

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

[[_2nd_order, _missing_x]]

18218

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

[[_2nd_order, _missing_x]]

18219

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

[[_2nd_order, _missing_x]]

18220

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

[[_2nd_order, _missing_x]]

18221

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

[[_2nd_order, _missing_x]]

18222

\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 0 \]

[[_2nd_order, _missing_x]]

18223

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

[[_2nd_order, _missing_x]]

18224

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

[[_2nd_order, _missing_x]]

18225

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

[[_2nd_order, _missing_x]]

18226

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

[[_2nd_order, _missing_x]]

18227

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

[[_2nd_order, _missing_x]]

18228

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

[[_2nd_order, _missing_x]]

18229

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

[[_2nd_order, _missing_x]]

18230

\[ {}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \]

[[_2nd_order, _missing_x]]

18231

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

[[_2nd_order, _missing_x]]

18232

\[ {}16 y^{\prime \prime }-8 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

18233

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

[[_2nd_order, _missing_x]]

18234

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

[[_2nd_order, _missing_x]]

18235

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

[[_2nd_order, _missing_x]]

18236

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

[[_2nd_order, _missing_x]]

18237

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

[[_2nd_order, _missing_x]]

18238

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

[[_2nd_order, _missing_x]]

18239

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

[[_2nd_order, _missing_x]]

18240

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

[[_2nd_order, _missing_x]]

18252

\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

18253

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

[[_2nd_order, _linear, _nonhomogeneous]]

18254

\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \]

[[_2nd_order, _with_linear_symmetries]]

18255

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \]

[[_2nd_order, _with_linear_symmetries]]

18256

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \]

[[_2nd_order, _with_linear_symmetries]]

18257

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18258

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

[[_2nd_order, _linear, _nonhomogeneous]]

18259

\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

[[_2nd_order, _missing_y]]

18260

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

[[_2nd_order, _with_linear_symmetries]]

18261

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

[[_2nd_order, _linear, _nonhomogeneous]]

18262

\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

[[_2nd_order, _missing_y]]

18263

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

[[_2nd_order, _linear, _nonhomogeneous]]

18264

\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \]

[[_2nd_order, _linear, _nonhomogeneous]]

18265

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18266

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

[[_2nd_order, _with_linear_symmetries]]

18267

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

[[_2nd_order, _with_linear_symmetries]]

18268

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

[[_2nd_order, _linear, _nonhomogeneous]]

18269

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

[[_2nd_order, _linear, _nonhomogeneous]]

18270

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18271

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

[[_2nd_order, _linear, _nonhomogeneous]]

18272

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

[[_2nd_order, _with_linear_symmetries]]

18273

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

[[_2nd_order, _linear, _nonhomogeneous]]

18274

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

[[_2nd_order, _linear, _nonhomogeneous]]

18275

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

[[_2nd_order, _linear, _nonhomogeneous]]

18276

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

[[_2nd_order, _linear, _nonhomogeneous]]

18277

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

[[_2nd_order, _linear, _nonhomogeneous]]

18278

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

[[_2nd_order, _linear, _nonhomogeneous]]

18279

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

[[_2nd_order, _linear, _nonhomogeneous]]

18280

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

[[_2nd_order, _linear, _nonhomogeneous]]

18309

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

[[_2nd_order, _with_linear_symmetries]]

18310

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

[[_2nd_order, _linear, _nonhomogeneous]]

18311

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18312

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

[[_2nd_order, _with_linear_symmetries]]

18313

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

[[_2nd_order, _with_linear_symmetries]]

18314

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x} \]

[[_2nd_order, _with_linear_symmetries]]

18315

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

[[_2nd_order, _linear, _nonhomogeneous]]

18317

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

[[_2nd_order, _linear, _nonhomogeneous]]

18320

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

[[_2nd_order, _linear, _nonhomogeneous]]

18321

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

[[_2nd_order, _linear, _nonhomogeneous]]

18324

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

[[_2nd_order, _linear, _nonhomogeneous]]

18325

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18326

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

[[_2nd_order, _linear, _nonhomogeneous]]

18335

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

[[_2nd_order, _linear, _nonhomogeneous]]

18446

\[ {}x^{\prime \prime }-5 x^{\prime }+6 x = 0 \]

[[_2nd_order, _missing_x]]

18447

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

[[_2nd_order, _missing_x]]

18448

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

[[_2nd_order, _missing_x]]

18449

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

[[_2nd_order, _missing_x]]

18450

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

[[_2nd_order, _missing_x]]

18451

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

[[_2nd_order, _missing_x]]

18452

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

[[_2nd_order, _missing_x]]

18453

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

[[_2nd_order, _missing_x]]

18454

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

[[_2nd_order, _with_linear_symmetries]]

18455

\[ {}x^{\prime \prime }-x = {\mathrm e}^{t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

18456

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

[[_2nd_order, _linear, _nonhomogeneous]]

18457

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

[[_2nd_order, _linear, _nonhomogeneous]]

18458

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

[[_2nd_order, _linear, _nonhomogeneous]]

18459

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

[[_2nd_order, _linear, _nonhomogeneous]]

18494

\[ {}\theta ^{\prime \prime } = -p^{2} \theta \]

[[_2nd_order, _missing_x]]

18509

\[ {}\theta ^{\prime \prime }-p^{2} \theta = 0 \]

[[_2nd_order, _missing_x]]

18510

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

[[_2nd_order, _missing_x]]

18511

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

[[_2nd_order, _missing_x]]

18512

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

[[_2nd_order, _missing_x]]

18514

\[ {}v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u} \]

[[_2nd_order, _with_linear_symmetries]]

18515

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

[[_2nd_order, _linear, _nonhomogeneous]]

18516

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

[[_2nd_order, _linear, _nonhomogeneous]]

18528

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

[[_2nd_order, _missing_x]]

18536

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

[[_2nd_order, _with_linear_symmetries]]

18584

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

[[_2nd_order, _missing_x]]

18585

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

[[_2nd_order, _missing_x]]

18593

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

[[_2nd_order, _with_linear_symmetries]]

18595

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

[[_2nd_order, _with_linear_symmetries]]

18596

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

[[_2nd_order, _with_linear_symmetries]]

18599

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

[[_2nd_order, _with_linear_symmetries]]

18600

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

[[_2nd_order, _with_linear_symmetries]]

18601

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

[[_2nd_order, _linear, _nonhomogeneous]]

18603

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

[[_2nd_order, _linear, _nonhomogeneous]]

18607

\[ {}e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2} \]

[[_2nd_order, _quadrature]]

18608

\[ {}e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \]

[[_2nd_order, _quadrature]]

18609

\[ {}e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \]

[[_2nd_order, _quadrature]]

18610

\[ {}e y^{\prime \prime } = -P \left (L -x \right ) \]

[[_2nd_order, _quadrature]]

18611

\[ {}e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \]

[[_2nd_order, _quadrature]]

18612

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

[[_2nd_order, _missing_x]]

18627

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

[[_2nd_order, _quadrature]]

18629

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

[[_2nd_order, _missing_x]]

18635

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

[[_2nd_order, _missing_y]]

18655

\[ {}y^{\prime \prime }-k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

18796

\[ {}y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

[[_2nd_order, _missing_x]]

18797

\[ {}y^{\prime \prime }-m^{2} y = 0 \]

[[_2nd_order, _missing_x]]

18798

\[ {}2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

[[_2nd_order, _missing_x]]

18799

\[ {}9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

[[_2nd_order, _missing_x]]

18802

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

18805

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

18806

\[ {}y^{\prime \prime }-y = 5 x +2 \]

[[_2nd_order, _with_linear_symmetries]]

18807

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

18811

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}} \]

[[_2nd_order, _with_linear_symmetries]]

18815

\[ {}y^{\prime \prime }+a^{2} y = \cos \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18816

\[ {}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18819

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18820

\[ {}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18821

\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18822

\[ {}y^{\prime \prime }-y = x^{2} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18826

\[ {}y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18827

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x} \]

[[_2nd_order, _with_linear_symmetries]]

18828

\[ {}y^{\prime \prime }-a^{2} y = {\mathrm e}^{a x}+{\mathrm e}^{n x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18834

\[ {}y^{\prime \prime }+a^{2} y = \sec \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18835

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18836

\[ {}y^{\prime \prime }+n^{2} y = x^{4} {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18840

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18842

\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18846

\[ {}y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

18847

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

18849

\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 20 x \]

[[_2nd_order, _with_linear_symmetries]]

18885

\[ {}y^{\prime \prime } = x^{2} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

18886

\[ {}y^{\prime \prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

18922

\[ {}y^{\prime \prime } = \frac {a}{x} \]

[[_2nd_order, _quadrature]]

18925

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

18928

\[ {}a y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

19088

\[ {}y^{\prime \prime }-n^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19090

\[ {}2 x^{\prime \prime }+5 x^{\prime }-12 x = 0 \]

[[_2nd_order, _missing_x]]

19091

\[ {}y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

[[_2nd_order, _missing_x]]

19092

\[ {}9 x^{\prime \prime }+18 x^{\prime }-16 x = 0 \]

[[_2nd_order, _missing_x]]

19094

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

19102

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

19103

\[ {}y^{\prime \prime }-y = 5 x +2 \]

[[_2nd_order, _with_linear_symmetries]]

19104

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

19105

\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19106

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}} \]

[[_2nd_order, _with_linear_symmetries]]

19107

\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x} \]

[[_2nd_order, _with_linear_symmetries]]

19108

\[ {}y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x} \]

[[_2nd_order, _with_linear_symmetries]]

19109

\[ {}y^{\prime \prime }+9 y = \cos \left (2 x \right )+\sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19110

\[ {}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )+\cos \left (b x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19111

\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{x}+\sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19113

\[ {}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19114

\[ {}y^{\prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19120

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19121

\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19122

\[ {}y^{\prime \prime }-y = \cosh \left (x \right ) \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19125

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19126

\[ {}y^{\prime \prime }+2 y^{\prime }+y = x \cos \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19129

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19130

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19131

\[ {}y^{\prime \prime }+y = {\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19135

\[ {}y^{\prime \prime }+y = 3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19138

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0 \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

19295

\[ {}y^{\prime \prime } = \sin \left (x \right )+x \]

[[_2nd_order, _quadrature]]

19296

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

19299

\[ {}y^{\prime \prime } = \frac {a}{x} \]

[[_2nd_order, _quadrature]]

19303

\[ {}y^{\prime \prime } = y \]

[[_2nd_order, _missing_x]]

19305

\[ {}y^{\prime \prime }-a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19311

\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x} \]

[[_2nd_order, _missing_y]]

19329

\[ {}a y^{\prime \prime } = y^{\prime } \]

[[_2nd_order, _missing_x]]

19351

\[ {}y^{\prime \prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19402

\[ {}y^{\prime \prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

19403

\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19404

\[ {}y^{\prime \prime }+4 y = 4 \tan \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19406

\[ {}y^{\prime \prime }-y = \frac {2}{{\mathrm e}^{x}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19458

\[ {}2 y^{\prime \prime }+9 y^{\prime }-18 y = 0 \]

[[_2nd_order, _missing_x]]

19462

\[ {}y^{\prime \prime }+n^{2} y = \sec \left (n x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19464

\[ {}y^{\prime \prime }-4 y^{\prime }+y = a \cos \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19467

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19469

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

19470

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \sinh \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19471

\[ {}y^{\prime \prime }+a^{2} y = \cos \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19472

\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

19532

\[ {}y^{\prime \prime } = x^{2} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

19533

\[ {}y^{\prime \prime } = \sec \left (x \right )^{2} \]

[[_2nd_order, _quadrature]]

19563

\[ {}y^{\prime \prime }+a^{2} y = \sec \left (a x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]