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

950

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

0.046

502

1463

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

0.046

503

2709

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

0.046

504

2790

\begin{align*} x^{\prime }&=a x-b x y \\ y^{\prime }&=-c y+d x y \\ z^{\prime }&=z+x^{2}+y^{2} \\ \end{align*}

0.046

505

2817

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

0.046

506

3091

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

0.046

507

3795

\begin{align*} y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y&=0 \\ \end{align*}

0.046

508

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*}

0.046

509

6630

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

0.046

510

6653

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

0.046

511

6752

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

0.046

512

6757

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

0.046

513

6761

\begin{align*} -3 y^{\prime }+11 y^{\prime \prime }-12 y^{\prime \prime \prime }+4 y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.046

514

8929

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

0.046

515

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*}

0.046

516

9294

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

0.046

517

9361

\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}
Series expansion around \(x=0\).

0.046

518

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*}

0.046

519

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*}

0.046

520

12810

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

0.046

521

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*}

0.046

522

13133

\begin{align*} x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24} \\ y^{\prime }&=2 x y-3 z \\ z^{\prime }&=3 x z-\frac {y^{2}}{6} \\ \end{align*}

0.046

523

13135

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

0.046

524

14349

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

0.046

525

14832

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

0.046

526

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*}

0.046

527

17549

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

0.046

528

18140

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

0.046

529

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*}

0.046

530

18982

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

0.046

531

20063

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

0.046

532

20591

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

0.046

533

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*}

0.046

534

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*}

0.046

535

951

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

0.047

536

1058

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

0.047

537

1464

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

0.047

538

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

539

4536

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

0.047

540

6649

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

0.047

541

6656

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

0.047

542

6740

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

0.047

543

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*}

0.047

544

6748

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

0.047

545

7053

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

0.047

546

9303

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

0.047

547

12718

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

0.047

548

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*}

0.047

549

13093

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

0.047

550

13099

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

0.047

551

13100

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

0.047

552

14422

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

0.047

553

15069

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

0.047

554

15398

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

0.047

555

16440

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

0.047

556

16542

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

0.047

557

16733

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

0.047

558

20041

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

0.047

559

22125

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

0.047

560

23342

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

0.047

561

25145

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

0.047

562

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*}

0.047

563

4557

\begin{align*} x^{\prime \prime }+2 x-2 y^{\prime }&=0 \\ 3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.048

564

6743

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

0.048

565

9295

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

0.048

566

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*}

0.048

567

13112

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

0.048

568

15420

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

0.048

569

15498

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

0.048

570

15751

\begin{align*} y_{1}^{\prime }&=2 x y_{1}-x^{2} y_{2}+4 x \\ y_{2}^{\prime }&={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \\ \end{align*}

0.048

571

16526

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

0.048

572

22112

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

0.048

573

24414

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

0.048

574

303

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

0.049

575

2712

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

0.049

576

4143

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

0.049

577

4147

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

0.049

578

6742

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

0.049

579

6753

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

0.049

580

6755

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

0.049

581

6774

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

0.049

582

7057

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

0.049

583

7067

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

0.049

584

7274

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

0.049

585

8916

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

0.049

586

8919

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

0.049

587

9081

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

0.049

588

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*}

0.049

589

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 (t \cos \left (t \right )-\sin \left (t \right )\right ) x+t \left (1-t \cos \left (t \right )\right ) y \\ \end{align*}

0.049

590

13130

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

0.049

591

13134

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

0.049

592

14423

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

0.049

593

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*}

0.049

594

16400

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

0.049

595

16465

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

0.049

596

16487

\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y&=0 \\ \end{align*}

0.049

597

16533

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

0.049

598

16543

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

0.049

599

18124

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

0.049

600

21252

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

0.049