2.3.4 Problems 301 to 400

Table 2.551: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

301

6769

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

0.043

302

8054

\begin{align*} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=8 \\ \end{align*}

0.043

303

8760

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

0.043

304

12726

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

0.043

305

12753

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

0.043

306

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*}

0.043

307

12757

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

0.043

308

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*}

0.043

309

12767

\begin{align*} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

0.043

310

12768

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

0.043

311

12776

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

0.043

312

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*}

0.043

313

12833

\begin{align*} x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\ \end{align*}

0.043

314

17422

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

0.043

315

20138

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

0.043

316

20335

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

0.043

317

21780

\begin{align*} x^{\prime }&=\sin \left (x\right )-4 y \\ y^{\prime }&=\sin \left (2 x\right )-5 y \\ \end{align*}

0.043

318

21783

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

0.043

319

23241

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

0.043

320

23796

\begin{align*} x^{\prime }&=5 x-6 y+x y \\ y^{\prime }&=6 x-7 y-x y \\ \end{align*}

0.043

321

23798

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

0.043

322

26135

\begin{align*} x^{\prime }&=-2 x+y+x \,y^{2} \\ y^{\prime }&=-7 x-2 y-7 y \,x^{2} \\ \end{align*}

0.043

323

284

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

0.044

324

285

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

0.044

325

943

\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}

0.044

326

2791

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

0.044

327

3097

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

0.044

328

4572

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

0.044

329

6723

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

0.044

330

6798

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

0.044

331

9306

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

0.044

332

12748

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

0.044

333

12749

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

0.044

334

12789

\begin{align*} y^{\prime \prime \prime \prime }+\left (a \,x^{2}+b \lambda +c \right ) y^{\prime \prime }+\left (a \,x^{2}+\beta \lambda +\gamma \right ) y&=0 \\ \end{align*}

0.044

335

13117

\begin{align*} x^{\prime }&=x \left (a \left (p x+q y\right )+\alpha \right ) \\ y^{\prime }&=y \left (\beta +b \left (p x+q y\right )\right ) \\ \end{align*}

0.044

336

14171

\begin{align*} 2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 y y^{\prime } x +6 y^{2}&=0 \\ \end{align*}

0.044

337

18407

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

0.044

338

18708

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

0.044

339

18710

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

0.044

340

19543

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

0.044

341

20333

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

0.044

342

20336

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

0.044

343

20810

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

0.044

344

21192

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

0.044

345

21236

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

0.044

346

21308

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

0.044

347

22929

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

0.044

348

23440

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

0.044

349

23469

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

0.044

350

25144

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

0.044

351

25919

\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+24 y^{\prime \prime }+10 y^{\prime }-25 y&=0 \\ \end{align*}

0.044

352

301

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

0.045

353

3089

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

0.045

354

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*}

0.045

355

6591

\begin{align*} h y^{2}+\operatorname {g1} y y^{\prime }+\operatorname {g0} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }+\operatorname {f0} {y^{\prime \prime }}^{2}&=0 \\ \end{align*}

0.045

356

8970

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

0.045

357

12752

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

0.045

358

12770

\begin{align*} x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-4 \left (1+3 x \right ) y&=0 \\ \end{align*}

0.045

359

12803

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

0.045

360

13078

\begin{align*} x^{\prime }+\left (a x+b y\right ) f \left (t \right )&=g \left (t \right ) \\ y^{\prime }+\left (c x+d y\right ) f \left (t \right )&=h \left (t \right ) \\ \end{align*}

0.045

361

13121

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

0.045

362

13127

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

0.045

363

15498

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

0.045

364

15738

\begin{align*} y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}

0.045

365

15739

\begin{align*} y_{1}^{\prime }&={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }&=\frac {y_{1}}{\left (x -2\right )^{2}} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (3\right ) &= 1 \\ y_{2} \left (3\right ) &= 0 \\ \end{align*}

0.045

366

18408

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

0.045

367

19062

\begin{align*} x^{\prime }&=1+5 y \\ y^{\prime }&=1-6 x^{2} \\ \end{align*}

0.045

368

19212

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

0.045

369

25928

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

0.045

370

282

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

0.046

371

302

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\ \end{align*}

0.046

372

949

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

0.046

373

3068

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\ \end{align*}

0.046

374

3071

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

0.046

375

3079

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

0.046

376

3085

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

0.046

377

4535

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

0.046

378

6680

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

0.046

379

6706

\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*}

0.046

380

7983

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

0.046

381

8058

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

0.046

382

12735

\begin{align*} 2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y&=0 \\ \end{align*}

0.046

383

12750

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

0.046

384

12751

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

0.046

385

15069

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

0.046

386

15420

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

0.046

387

18132

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

0.046

388

18425

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

0.046

389

21186

\begin{align*} x^{\prime \prime \prime \prime }-6 x^{\prime \prime }+5 x&=0 \\ \end{align*}

0.046

390

21249

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

0.046

391

23800

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

0.046

392

25921

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-9 y^{\prime \prime }+8 y^{\prime }-2 y&=0 \\ \end{align*}

0.046

393

25929

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

0.046

394

951

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

0.047

395

2794

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

0.047

396

6609

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

0.047

397

6772

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

0.047

398

12711

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

0.047

399

13123

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

0.047

400

15734

\begin{align*} y_{1}^{\prime }&=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }&=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (-1\right ) &= 3 \\ y_{2} \left (-1\right ) &= -3 \\ \end{align*}

0.047