2.2.4 Problems 301 to 400

Table 2.9: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

301

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

[[_3rd_order, _missing_x]]

0.075

302

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

[[_high_order, _missing_x]]

0.043

303

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-54 y = 0 \]

[[_3rd_order, _missing_x]]

0.086

304

\[ {}3 y^{\prime \prime \prime }-2 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

[[_3rd_order, _missing_x]]

0.092

305

\[ {}6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+25 y^{\prime \prime }+20 y^{\prime }+4 y = 0 \]

[[_high_order, _missing_x]]

0.089

306

\[ {}9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y = 0 \]

[[_3rd_order, _missing_x]]

0.089

307

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

[[_high_order, _missing_x]]

0.086

308

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.102

309

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

[[_2nd_order, _missing_x]]

0.794

310

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

[[_2nd_order, _missing_x]]

0.778

311

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

[[_2nd_order, _missing_x]]

4.661

312

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

[[_3rd_order, _missing_x]]

0.131

313

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

[[_high_order, _missing_x]]

0.100

314

\[ {}a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.624

315

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

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

1.515

316

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

[[_Emden, _Fowler]]

2.373

317

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x = 0 \]

[[_3rd_order, _missing_y]]

0.124

318

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

[[_3rd_order, _missing_y]]

0.110

319

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

[[_3rd_order, _missing_y]]

0.102

320

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

[[_3rd_order, _missing_y]]

0.116

321

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y = 0 \]

[[_3rd_order, _exact, _linear, _homogeneous]]

0.706

322

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

[[_2nd_order, _with_linear_symmetries]]

2.610

323

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

[[_2nd_order, _with_linear_symmetries]]

29.700

324

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.345

325

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.475

326

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

[[_2nd_order, _linear, _nonhomogeneous]]

76.602

327

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

[[_2nd_order, _with_linear_symmetries]]

30.507

328

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

[[_2nd_order, _linear, _nonhomogeneous]]

8.134

329

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.553

330

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.026

331

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

[[_2nd_order, _linear, _nonhomogeneous]]

7.385

332

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

[[_3rd_order, _missing_y]]

0.111

333

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

[[_3rd_order, _missing_y]]

0.370

334

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

[[_2nd_order, _linear, _nonhomogeneous]]

18.222

335

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

[[_high_order, _linear, _nonhomogeneous]]

0.073

336

\[ {}y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }-y = 17 \]

[[_high_order, _missing_x]]

0.096

337

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.782

338

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.982

339

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

[[_high_order, _linear, _nonhomogeneous]]

0.227

340

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

[[_high_order, _missing_y]]

0.184

341

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

[[_3rd_order, _with_linear_symmetries]]

0.132

342

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.322

343

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

[[_high_order, _missing_y]]

0.093

344

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.777

345

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

[[_3rd_order, _missing_y]]

0.096

346

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.325

347

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

[[_2nd_order, _linear, _nonhomogeneous]]

15.906

348

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

[[_high_order, _linear, _nonhomogeneous]]

1.171

349

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

[[_high_order, _missing_y]]

0.594

350

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

[[_high_order, _linear, _nonhomogeneous]]

0.166

351

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

[[_2nd_order, _with_linear_symmetries]]

3.691

352

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

[[_2nd_order, _with_linear_symmetries]]

1.091

353

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.855

354

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.548

355

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

[[_2nd_order, _with_linear_symmetries]]

9.055

356

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

[[_high_order, _missing_y]]

0.106

357

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

[[_3rd_order, _missing_y]]

0.106

358

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

[[_2nd_order, _linear, _nonhomogeneous]]

10.144

359

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

[[_3rd_order, _missing_y]]

0.102

360

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

[[_high_order, _missing_x]]

0.118

361

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }-2 y = 8 x^{5} \]
i.c.

[[_high_order, _linear, _nonhomogeneous]]

0.164

362

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

[[_high_order, _linear, _nonhomogeneous]]

0.187

363

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

[[_2nd_order, _linear, _nonhomogeneous]]

76.704

364

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.017

365

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

[[_2nd_order, _linear, _nonhomogeneous]]

6.765

366

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

[[_2nd_order, _with_linear_symmetries]]

0.800

367

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

[[_2nd_order, _with_linear_symmetries]]

0.848

368

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

[[_2nd_order, _with_linear_symmetries]]

0.888

369

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

[[_2nd_order, _linear, _nonhomogeneous]]

6.762

370

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.148

371

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.861

372

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.502

373

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.395

374

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.189

375

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.095

376

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.983

377

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

[[_2nd_order, _with_linear_symmetries]]

1.911

378

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

[[_2nd_order, _with_linear_symmetries]]

1.035

379

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

[[_2nd_order, _with_linear_symmetries]]

1.895

380

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

[[_2nd_order, _with_linear_symmetries]]

3.245

381

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

[[_2nd_order, _with_linear_symmetries]]

1.471

382

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.057

383

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.771

384

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.199

385

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.131

386

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

[[_2nd_order, _linear, _nonhomogeneous]]

6.642

387

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

[[_2nd_order, _linear, _nonhomogeneous]]

87.065

388

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.730

389

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

[[_2nd_order, _linear, _nonhomogeneous]]

74.704

390

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

[[_2nd_order, _linear, _nonhomogeneous]]

19.013

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]]

376.342

392

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

[[_2nd_order, _linear, _nonhomogeneous]]

9.716

393

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

[[_2nd_order, _linear, _nonhomogeneous]]

27.602

394

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

[[_2nd_order, _linear, _nonhomogeneous]]

17.607

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]]

17.809

396

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

[[_2nd_order, _linear, _nonhomogeneous]]

23.434

397

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

[[_2nd_order, _linear, _nonhomogeneous]]

23.439

398

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

[[_2nd_order, _linear, _nonhomogeneous]]

63.152

399

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

[[_2nd_order, _linear, _nonhomogeneous]]

71.725

400

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

[_quadrature]

0.304