2.3.6 Problems 501 to 600

Table 2.555: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

501

25392

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

0.051

502

25926

\begin{align*} y^{\left (6\right )}+18 y^{\prime \prime \prime \prime }+81 y^{\prime \prime }&=0 \\ \end{align*}

0.051

503

286

\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}

0.052

504

306

\begin{align*} 9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y&=0 \\ \end{align*}

0.052

505

604

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

0.052

506

6685

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

0.052

507

7985

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}

0.052

508

12743

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

0.052

509

12808

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y&=0 \\ \end{align*}

0.052

510

13124

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

0.052

511

15398

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

0.052

512

18139

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

0.052

513

19225

\begin{align*} t x^{\prime }+6 x-y-3 z&=0 \\ y^{\prime } t +23 x-6 y-9 z&=0 \\ t z^{\prime }+x+y-2 z&=0 \\ \end{align*}

0.052

514

19531

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

0.052

515

20209

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

0.052

516

20529

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

0.052

517

21784

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

0.052

518

937

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

0.053

519

953

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

0.053

520

3076

\begin{align*} 2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y&=0 \\ \end{align*}

0.053

521

3084

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime }&=0 \\ \end{align*}

0.053

522

3794

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

0.053

523

7051

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

0.053

524

8915

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

0.053

525

9293

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

0.053

526

9294

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

0.053

527

12775

\begin{align*} x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y&=0 \\ \end{align*}

0.053

528

12794

\begin{align*} x y^{\prime \prime \prime \prime }-\left (6 x^{2}+1\right ) y^{\prime \prime \prime }+12 x^{3} y^{\prime \prime }-\left (9 x^{2}-7\right ) x^{2} y^{\prime }+2 \left (x^{2}-3\right ) x^{3} y&=0 \\ \end{align*}

0.053

529

14864

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

0.053

530

15424

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

0.053

531

15671

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

0.053

532

16543

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

0.053

533

18427

\begin{align*} x^{\prime }&=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\ y^{\prime }&=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.053

534

19530

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

0.053

535

19534

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

0.053

536

20609

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

0.053

537

20779

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

0.053

538

23240

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

0.053

539

24036

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

0.053

540

24441

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

0.053

541

305

\begin{align*} 6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+25 y^{\prime \prime }+20 y^{\prime }+4 y&=0 \\ \end{align*}

0.054

542

3082

\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y&=0 \\ \end{align*}

0.054

543

3101

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

0.054

544

6759

\begin{align*} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.054

545

10051

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

0.054

546

12708

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

0.054

547

17540

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

0.054

548

18980

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

0.054

549

20534

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

0.054

550

21311

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

0.054

551

22799

\begin{align*} y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \\ \end{align*}

0.054

552

22892

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

0.054

553

24445

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

0.054

554

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*}

0.054

555

3102

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y&=0 \\ \end{align*}

0.055

556

3703

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y&=0 \\ \end{align*}

0.055

557

6713

\begin{align*} -8 y+3 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right )^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

0.055

558

9297

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

0.055

559

13034

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

0.055

560

18146

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

0.055

561

18976

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

0.055

562

18981

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

0.055

563

20155

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

0.055

564

24414

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-15 y^{\prime }&=0 \\ \end{align*}

0.055

565

24420

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

0.055

566

24423

\begin{align*} 4 y^{\prime \prime \prime }-13 y^{\prime }-6 y&=0 \\ \end{align*}

0.055

567

24446

\begin{align*} 4 y^{\prime \prime \prime }-27 y^{\prime }+27 y&=0 \\ \end{align*}

0.055

568

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*}

0.055

569

25520

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

0.055

570

287

\begin{align*} 6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \\ \end{align*}

0.056

571

3083

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y&=0 \\ \end{align*}

0.056

572

3699

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

0.056

573

3823

\begin{align*} x_{1}^{\prime }&=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2} \\ x_{2}^{\prime }&=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 4 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.056

574

4150

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

0.056

575

4447

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

0.056

576

6785

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

0.056

577

8920

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

0.056

578

10902

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

0.056

579

13113

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

0.056

580

15426

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

0.056

581

16440

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

0.056

582

16733

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

0.056

583

20341

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

0.056

584

20754

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

0.056

585

21779

\begin{align*} x^{\prime }&=x+4 y-y^{2} \\ y^{\prime }&=6 x-y+2 x y \\ \end{align*}

0.056

586

22259

\begin{align*} w^{\prime \prime }-y+2 z&=3 \,{\mathrm e}^{-t} \\ -2 w^{\prime }+2 y^{\prime }+z&=0 \\ 2 w^{\prime }-2 y+z^{\prime }+2 z^{\prime \prime }&=0 \\ \end{align*}
With initial conditions
\begin{align*} y \left (0\right ) &= 2 \\ z \left (0\right ) &= 2 \\ z^{\prime }\left (0\right ) &= -2 \\ w \left (0\right ) &= 1 \\ w^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.056

587

22800

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

0.056

588

23557

\begin{align*} x_{1}^{\prime }&=2 \sin \left (t \right ) x_{1}+\ln \left (t \right ) x_{2} \\ x_{2}^{\prime }&=\frac {x_{1}}{-2+t}+\frac {{\mathrm e}^{t} x_{2}}{1+t} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (3\right ) &= 0 \\ x_{2} \left (3\right ) &= 0 \\ \end{align*}

0.056

589

24443

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

0.056

590

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*}

0.056

591

3705

\begin{align*} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \\ \end{align*}

0.057

592

6625

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

0.057

593

6747

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

0.057

594

10960

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

0.057

595

12715

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

0.057

596

12769

\begin{align*} 2 \left (x -\operatorname {a1} \right ) \left (x -\operatorname {a2} \right ) \left (x -\operatorname {a3} \right ) y^{\prime \prime \prime }+\left (9 x^{2}-6 \left (\operatorname {a1} +\operatorname {a2} +\operatorname {a3} \right ) x +3 \operatorname {a1} \operatorname {a2} +3 \operatorname {a1} \operatorname {a3} +3 \operatorname {a2} \operatorname {a3} \right ) y^{\prime \prime }-2 \left (\left (n^{2}+n -3\right ) x +b \right ) y^{\prime }-n \left (n +1\right ) y&=0 \\ \end{align*}

0.057

597

12809

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y&=0 \\ \end{align*}

0.057

598

13096

\begin{align*} a_{1} x^{\prime \prime }+b_{1} x^{\prime }+c_{1} x-A y^{\prime }&=B \,{\mathrm e}^{i \omega t} \\ a_{2} y^{\prime \prime }+b_{2} y^{\prime }+c_{2} y+A x^{\prime }&=0 \\ \end{align*}

0.057

599

19174

\begin{align*} -2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=x^{4}+12 \\ \end{align*}

0.057

600

20337

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

0.057