2.3.36 Problems 3501 to 3600

Table 2.603: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

3501

19123

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

0.273

3502

21204

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

0.273

3503

21641

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

0.273

3504

25239

\begin{align*} t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \\ \end{align*}
Using Laplace transform method.

0.273

3505

1090

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

0.274

3506

2613

\begin{align*} y^{\prime \prime }-t^{3} y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.274

3507

3954

\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align*}
Using Laplace transform method.

0.274

3508

10014

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

0.274

3509

10965

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

0.274

3510

12778

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

0.274

3511

16005

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

0.274

3512

21220

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

0.274

3513

21569

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

0.274

3514

23092

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

0.274

3515

1085

\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align*}
Series expansion around \(x=3\).

0.275

3516

1491

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

0.275

3517

1634

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

0.275

3518

2226

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=12 x^{2} \\ \end{align*}

0.275

3519

6931

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

0.275

3520

8481

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

0.275

3521

10535

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

0.275

3522

10808

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

0.275

3523

21912

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.275

3524

22880

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

0.275

3525

409

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

0.276

3526

6767

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

0.276

3527

6768

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

0.276

3528

9452

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}
Using Laplace transform method.

0.276

3529

10510

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

0.276

3530

10617

\begin{align*} 9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}

0.276

3531

10651

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

0.276

3532

11024

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

0.276

3533

12843

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

0.276

3534

15723

\begin{align*} y^{\prime }+3 y&=\delta \left (x -2\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.276

3535

19646

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

0.276

3536

19651

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

0.276

3537

20611

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

0.276

3538

23831

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

0.276

3539

24619

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+27 y^{\prime }+27 y&=15 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}

0.276

3540

25164

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

0.276

3541

407

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

0.277

3542

1076

\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.277

3543

1787

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

0.277

3544

10729

\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}

0.277

3545

10807

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}

0.277

3546

11018

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

0.277

3547

12920

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

0.277

3548

16778

\begin{align*} y^{\prime \prime }+8 y^{\prime }+17 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -12 \\ \end{align*}
Using Laplace transform method.

0.277

3549

16852

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

0.277

3550

17630

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

0.277

3551

408

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

0.278

3552

1075

\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.278

3553

5380

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

0.278

3554

6970

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

0.278

3555

10329

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

0.278

3556

13195

\(\left [\begin {array}{ccc} 3 & -2 & 1 \\ 1 & 0 & 1 \\ -1 & 1 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.278

3557

16006

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

0.278

3558

18385

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

0.278

3559

23638

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=2 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.278

3560

24017

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

0.278

3561

405

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

0.279

3562

554

\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25}&=6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.279

3563

4368

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

0.279

3564

5383

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

0.279

3565

5464

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

0.279

3566

6331

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

0.279

3567

11057

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}

0.279

3568

15985

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

0.279

3569

18908

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.279

3570

20393

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

0.279

3571

20416

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

0.279

3572

20538

\begin{align*} x^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}

0.279

3573

21706

\begin{align*} y+y^{\prime }&=t \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.279

3574

24845

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

0.279

3575

25175

\begin{align*} y_{1}^{\prime }-y_{1}&=-2 y_{2} \\ y_{2}^{\prime }-y_{2}&=2 y_{1} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}

0.279

3576

410

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

0.280

3577

963

\begin{align*} x_{1}^{\prime }&=6 x_{1} \\ x_{2}^{\prime }&=-3 x_{1}-x_{2} \\ \end{align*}

0.280

3578

1005

\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+7 x_{2} \\ \end{align*}

0.280

3579

3241

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

0.280

3580

7882

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

0.280

3581

8128

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

0.280

3582

9030

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

0.280

3583

10682

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y&=0 \\ \end{align*}

0.280

3584

10805

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

0.280

3585

11243

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

0.280

3586

16398

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

0.280

3587

18889

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=t^{2}+7 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.280

3588

21219

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

0.280

3589

21536

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

0.280

3590

21639

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

0.280

3591

22936

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

0.280

3592

23634

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

0.280

3593

25643

\begin{align*} y^{\prime }&=-\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.280

3594

535

\begin{align*} x^{\prime \prime }+4 x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.281

3595

3340

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

0.281

3596

4374

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

0.281

3597

4520

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=54 t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.281

3598

6765

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

0.281

3599

8567

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

0.281

3600

10992

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

0.281