2.3.4 Problems 301 to 400

Table 2.581: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

301

19182

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}

0.049

302

19530

\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}

0.049

303

19534

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.049

304

21241

\begin{align*} x x^{\prime }+y&=2 t \\ y^{\prime }+2 x^{2}&=1 \\ \end{align*}

0.049

305

21253

\begin{align*} x^{\prime }&=x \left (3-y\right ) \\ y^{\prime }&=y \left (x-5\right ) \\ \end{align*}

0.049

306

21925

\begin{align*} x^{\prime \prime }&=1 \\ x^{\prime }+x+y^{\prime \prime }-9 y+z^{\prime }+z&=0 \\ 5 x+z^{\prime \prime }-4 z&=2 \\ \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.049

307

25393

\begin{align*} y_{1}^{\prime }&=-\frac {y_{2}}{t}+1 \\ y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {2 y_{2}}{t}-1 \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (1\right ) &= 2 \\ y_{2} \left (1\right ) &= 0 \\ \end{align*}

0.049

308

937

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}

0.050

309

2141

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.050

310

3097

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.050

311

12747

\begin{align*} a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.050

312

12802

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16}&=0 \\ \end{align*}

0.050

313

12832

\begin{align*} x^{10} y^{\left (5\right )}-a y&=0 \\ \end{align*}

0.050

314

18422

\begin{align*} x^{\prime }&=-\frac {1}{y} \\ y^{\prime }&=\frac {1}{x} \\ \end{align*}

0.050

315

18424

\begin{align*} x^{\prime }&=\frac {y}{x-y} \\ y^{\prime }&=\frac {x}{x-y} \\ \end{align*}

0.050

316

20063

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \\ \end{align*}

0.050

317

20335

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \\ \end{align*}

0.050

318

22266

\begin{align*} w^{\prime \prime }+y+z&=-1 \\ w+y^{\prime \prime }-z&=0 \\ -w-y^{\prime }+z^{\prime \prime }&=0 \\ \end{align*}

With initial conditions

\begin{align*} w \left (0\right ) &= 0 \\ w^{\prime }\left (0\right ) &= 1 \\ z \left (0\right ) &= -1 \\ z^{\prime }\left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.050

319

23990

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.050

320

25388

\begin{align*} y_{1}^{\prime }&=y_{1} t +y_{2} t \\ y_{2}^{\prime }&=-y_{1} t -y_{2} t \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 4 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}

0.050

321

25389

\begin{align*} y_{1}^{\prime }&=\frac {y_{1}}{t}+y_{2} \\ y_{2}^{\prime }&=-y_{1}+\frac {y_{2}}{t} \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (\pi \right ) &= 1 \\ y_{2} \left (\pi \right ) &= -1 \\ \end{align*}

0.050

322

25391

\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=\frac {y_{1}}{t}+\frac {y_{2}}{t} \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (1\right ) &= -3 \\ y_{2} \left (1\right ) &= 4 \\ \end{align*}

0.050

323

25396

\begin{align*} y_{1}^{\prime }&=y_{1} t +y_{2} t +4 t \\ y_{2}^{\prime }&=-y_{1} t -y_{2} t +4 t \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 4 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}

0.050

324

26489

\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}

0.050

325

26497

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.050

326

26780

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y&=0 \\ \end{align*}

0.050

327

280

\begin{align*} 5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \\ \end{align*}

0.051

328

3092

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}

0.051

329

12714

\begin{align*} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-a b y&=0 \\ \end{align*}

0.051

330

12723

\begin{align*} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

0.051

331

12731

\begin{align*} x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}

0.051

332

12756

\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime \prime }+3 \left (2 x -1\right ) y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a y&=0 \\ \end{align*}

0.051

333

12758

\begin{align*} x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y&=0 \\ \end{align*}

0.051

334

12768

\begin{align*} \left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (x +2\right ) y^{\prime \prime }+6 \left (x +1\right ) y^{\prime }-6 y&=0 \\ \end{align*}

0.051

335

12828

\begin{align*} x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y&=0 \\ \end{align*}

0.051

336

22258

\begin{align*} z^{\prime \prime }+y^{\prime }&=\cos \left (t \right ) \\ y^{\prime \prime }-z&=\sin \left (t \right ) \\ \end{align*}

With initial conditions

\begin{align*} y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ z \left (0\right ) &= -1 \\ z^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.051

337

22265

\begin{align*} w^{\prime \prime }-2 z&=0 \\ w^{\prime }+y^{\prime }-z&=2 t \\ w^{\prime }-2 y+z^{\prime \prime }&=0 \\ \end{align*}

With initial conditions

\begin{align*} w \left (0\right ) &= 0 \\ w^{\prime }\left (0\right ) &= 0 \\ z \left (0\right ) &= 1 \\ z^{\prime }\left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.051

338

23246

\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+y x&=0 \\ \end{align*}

0.051

339

23255

\begin{align*} x y^{\prime \prime \prime }+4 x y^{\prime \prime }-y x&=1 \\ \end{align*}

0.051

340

25688

\begin{align*} x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\ \end{align*}

0.051

341

26767

\begin{align*} x^{\prime }&=x+2 y-\sin \left (y\right )^{2} \\ y^{\prime }&=-x-3 y+x \left ({\mathrm e}^{\frac {x^{2}}{2}}-1\right ) \\ \end{align*}

0.051

342

26790

\begin{align*} y^{\prime \prime \prime \prime }+\alpha y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+3 y&=0 \\ \end{align*}

0.051

343

26795

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}

0.051

344

289

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}

0.052

345

3080

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=0 \\ \end{align*}

0.052

346

3497

\begin{align*} 2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}&=\sin \left (x \right ) \\ \end{align*}

0.052

347

7059

\begin{align*} 36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y&=0 \\ \end{align*}

0.052

348

7334

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}

0.052

349

12722

\begin{align*} y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y&=0 \\ \end{align*}

0.052

350

12734

\begin{align*} 2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y&=0 \\ \end{align*}

0.052

351

12762

\begin{align*} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.052

352

12788

\begin{align*} y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y&=0 \\ \end{align*}

0.052

353

12799

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}

0.052

354

13083

\begin{align*} t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }&=t \left (1-2 \sin \left (t \right )\right ) x+t^{2} y \\ t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }&=\left (\cos \left (t \right ) t -\sin \left (t \right )\right ) x+t \left (1-\cos \left (t \right ) t \right ) y \\ \end{align*}

0.052

355

13137

\begin{align*} \left (x-y\right ) \left (x-z\right ) x^{\prime }&=f \left (t \right ) \\ \left (-x+y\right ) \left (y-z\right ) y^{\prime }&=f \left (t \right ) \\ \left (-x+z\right ) \left (-y+z\right ) z^{\prime }&=f \left (t \right ) \\ \end{align*}

0.052

356

16440

\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}

0.052

357

19184

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.052

358

20040

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\ \end{align*}

0.052

359

20138

\begin{align*} a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.052

360

20329

\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

0.052

361

20333

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\ \end{align*}

0.052

362

20529

\begin{align*} 3 y x +y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=2 \\ \end{align*}

0.052

363

23227

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.052

364

26791

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+\alpha y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}

0.052

365

27598

\begin{align*} 2 y y^{\prime \prime \prime }&=y^{\prime } \\ \end{align*}

0.052

366

281

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}

0.053

367

298

\begin{align*} 2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}

0.053

368

299

\begin{align*} y^{\prime \prime \prime }+27 y&=0 \\ \end{align*}

0.053

369

953

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\ \end{align*}

0.053

370

2791

\begin{align*} x^{\prime }&=-x-x \,y^{2} \\ y^{\prime }&=-y-y \,x^{2} \\ z^{\prime }&=1-z+x^{2} \\ \end{align*}

0.053

371

3095

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y&=0 \\ \end{align*}

0.053

372

3096

\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ \end{align*}

0.053

373

4549

\begin{align*} x^{\prime }+4 x+2 y&=\frac {2}{{\mathrm e}^{t}-1} \\ 6 x-y^{\prime }+3 y&=\frac {3}{{\mathrm e}^{t}-1} \\ \end{align*}

0.053

374

12726

\begin{align*} y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y\right )&=0 \\ \end{align*}

0.053

375

12784

\begin{align*} y^{\prime \prime \prime \prime }+\lambda y&=0 \\ \end{align*}

0.053

376

13132

\begin{align*} x^{\prime }+y^{\prime }&=x y \\ y^{\prime }+z^{\prime }&=y z \\ x^{\prime }+z^{\prime }&=x z \\ \end{align*}

0.053

377

15736

\begin{align*} y_{1}^{\prime }&=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }&=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (1\right ) &= 1 \\ y_{2} \left (1\right ) &= -1 \\ \end{align*}

0.053

378

16543

\begin{align*} y^{\prime \prime \prime }+216 y&=0 \\ \end{align*}

0.053

379

18404

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}

0.053

380

18421

\begin{align*} x^{\prime }&=x^{2}+y^{2} \\ y^{\prime }&=2 x y \\ \end{align*}

0.053

381

19831

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.053

382

20340

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.053

383

20609

\begin{align*} y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime }+y x&=0 \\ \end{align*}

0.053

384

20699

\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}

0.053

385

21701

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+x y^{\prime }-y&=-\ln \left (x \right ) \\ \end{align*}

Series expansion around \(x=0\).

0.053

386

22906

\begin{align*} x^{\prime \prime }&=-2 y \\ y^{\prime }&=y-x^{\prime } \\ \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 10 \\ y \left (0\right ) &= 5 \\ \end{align*}

0.053

387

23240

\begin{align*} y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \\ \end{align*}

0.053

388

25361

\begin{align*} y_{1}^{\prime }&=t \sin \left (y_{1}\right )-y_{2} \\ y_{2}^{\prime }&=y_{1}+t \cos \left (y_{2}\right ) \\ \end{align*}

0.053

389

25390

\begin{align*} y_{1}^{\prime }&=\left (2 t +1\right ) y_{1}+2 y_{2} t \\ y_{2}^{\prime }&=-2 y_{1} t +\left (1-2 t \right ) y_{2} \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}

0.053

390

26105

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

0.053

391

26781

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}

0.053

392

26782

\begin{align*} y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+17 y^{\prime \prime }+17 y^{\prime }+6 y&=0 \\ \end{align*}

0.053

393

26783

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+12 y^{\prime }-10 y&=0 \\ \end{align*}

0.053

394

26799

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+16 y^{\prime \prime }+24 y^{\prime }+20 y&=0 \\ \end{align*}

0.053

395

2788

\begin{align*} x^{\prime }&=x-x^{2}-2 x y \\ y^{\prime }&=2 y-2 y^{2}-3 x y \\ \end{align*}

0.054

396

3070

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y&=0 \\ \end{align*}

0.054

397

9306

\begin{align*} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.054

398

10047

\begin{align*} y y^{\prime \prime }&=0 \\ \end{align*}

0.054

399

12765

\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} \left (x +3\right ) y^{\prime \prime }+5 \left (-6+x \right ) x y^{\prime }+\left (4 x +30\right ) y&=0 \\ \end{align*}

0.054

400

12801

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}

0.054