2.3.6 Problems 501 to 600

Table 2.543: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

501

6612

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

0.047

502

6625

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

0.047

503

6716

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

0.047

504

6722

\begin{align*} -4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

0.047

505

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*}

0.047

506

13126

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

0.047

507

15681

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

0.047

508

17421

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

0.047

509

17824

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

0.047

510

19175

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

0.047

511

19541

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

0.047

512

22314

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

0.047

513

22496

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

0.047

514

25151

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-25 y^{\prime }+50 y&=0 \\ \end{align*}

0.047

515

303

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-54 y&=0 \\ \end{align*}

0.048

516

2816

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

0.048

517

4144

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=0 \\ \end{align*}

0.048

518

6667

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

0.048

519

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*}

0.048

520

6785

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

0.048

521

6793

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

0.048

522

7048

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

0.048

523

9047

\begin{align*} y_{1}^{\prime }&=3 y_{1}+x y_{3} \\ y_{2}^{\prime }&=y_{2}+x^{3} y_{3} \\ y_{3}^{\prime }&=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \\ \end{align*}

0.048

524

10051

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

0.048

525

12711

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

0.048

526

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*}

0.048

527

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*}

0.048

528

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*}

0.048

529

16542

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

0.048

530

18970

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

0.048

531

18975

\begin{align*} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y&=\ln \left (t \right ) \\ \end{align*}

0.048

532

19529

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

0.048

533

19784

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

0.048

534

20043

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

0.048

535

20138

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

0.048

536

23365

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

0.048

537

25150

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

0.048

538

954

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

0.049

539

2114

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

0.049

540

2117

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

0.049

541

2120

\begin{align*} 27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y&=0 \\ \end{align*}

0.049

542

2813

\begin{align*} x^{\prime }&=x-x^{3}-x y \\ y^{\prime }&=2 y-y^{5}-y \,x^{4} \\ \end{align*}

0.049

543

2814

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

0.049

544

6630

\begin{align*} -15 y-7 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

0.049

545

6649

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

0.049

546

7271

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

0.049

547

8921

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

0.049

548

12716

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

0.049

549

12718

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y&=0 \\ \end{align*}

0.049

550

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*}

0.049

551

14093

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

0.049

552

19184

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

0.049

553

19535

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

0.049

554

19831

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

0.049

555

20063

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

0.049

556

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*}

0.049

557

21188

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

0.049

558

21192

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

0.049

559

21311

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

0.049

560

22112

\begin{align*} y^{\prime \prime \prime \prime }-9 y^{\prime \prime }+20 y&=0 \\ \end{align*}

0.049

561

22114

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

0.049

562

22329

\begin{align*} y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y \left (1\right ) &= 2 \\ y \left (2\right ) &= 9 \\ \end{align*}

0.049

563

22659

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

0.049

564

23107

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

0.049

565

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*}

0.049

566

25146

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

0.049

567

25520

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

0.049

568

25650

\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}

0.049

569

286

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

0.050

570

6660

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

0.050

571

6723

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

0.050

572

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*}

0.050

573

7045

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y&=0 \\ \end{align*}

0.050

574

7047

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

0.050

575

8915

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

0.050

576

12784

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

0.050

577

12805

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

0.050

578

12807

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

0.050

579

12826

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

0.050

580

15675

\begin{align*} 36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}

0.050

581

15680

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

0.050

582

19221

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

0.050

583

20699

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

0.050

584

21287

\begin{align*} x^{\prime }-x&=k \delta \left (t \right ) \\ x \left (0\right ) &= a \\ \end{align*}
Using Laplace transform method.

0.050

585

22116

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y&=0 \\ \end{align*}

0.050

586

23800

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

0.050

587

25147

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}

0.050

588

300

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y&=0 \\ \end{align*}

0.051

589

936

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

0.051

590

2119

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

0.051

591

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*}

0.051

592

6742

\begin{align*} 27 y-12 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.051

593

6743

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

0.051

594

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*}

0.051

595

6797

\begin{align*} 3 y^{2}+18 y y^{\prime } x +9 x^{2} {y^{\prime }}^{2}+9 x^{2} y y^{\prime \prime }+3 x^{3} y^{\prime } y^{\prime \prime }+x^{3} y y^{\prime \prime \prime }&=0 \\ \end{align*}

0.051

596

8927

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

0.051

597

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

598

15672

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

0.051

599

16440

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

0.051

600

16543

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

0.051