2.3.95 Problems 9401 to 9500

Table 2.763: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9401

3350

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

Series expansion around \(x=0\).

0.695

9402

4169

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

0.695

9403

7970

\begin{align*} y^{\prime \prime }+9 y&=x \cos \left (x \right ) \\ \end{align*}

0.695

9404

15265

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

0.695

9405

19650

\begin{align*} x^{\prime }&=x+y-5 t +2 \\ y^{\prime }&=4 x-2 y-8 t -8 \\ \end{align*}

0.695

9406

21293

\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=7 x-4 y \\ \end{align*}

0.695

9407

24773

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

0.695

9408

2277

\begin{align*} y_{1}^{\prime }&=y_{1}+10 y_{2}-12 y_{3} \\ y_{2}^{\prime }&=2 y_{1}+2 y_{2}+3 y_{3} \\ y_{3}^{\prime }&=2 y_{1}-y_{2}+6 y_{3} \\ \end{align*}

0.696

9409

3864

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

0.696

9410

4383

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

0.696

9411

13292

\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\mu x} y^{2}+\lambda y-a \,b^{2} {\mathrm e}^{\left (\mu +2 \lambda \right ) x} \\ \end{align*}

0.696

9412

15429

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

0.696

9413

21540

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

0.696

9414

27151

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}

0.696

9415

2276

\begin{align*} y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3} \\ y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3} \\ \end{align*}

0.697

9416

2278

\begin{align*} y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-4 y_{3} \\ y_{2}^{\prime }&=2 y_{1}-y_{2}+y_{3} \\ y_{3}^{\prime }&=2 y_{1}+3 y_{2}+y_{3} \\ \end{align*}

0.697

9417

3853

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=-b x_{1}-a x_{2} \\ \end{align*}

0.697

9418

4021

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

Series expansion around \(x=0\).

0.697

9419

7580

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y&=\cos \left (\omega t \right ) \\ \end{align*}

0.697

9420

7664

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

Series expansion around \(x=0\).

0.697

9421

9253

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

0.697

9422

10482

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

0.697

9423

17502

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{4}} \\ \end{align*}

0.697

9424

18728

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

0.697

9425

20378

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right )&=0 \\ y \left (\frac {\pi }{2}\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.697

9426

21526

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

0.697

9427

21551

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

0.697

9428

21902

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

Series expansion around \(x=0\).

0.697

9429

23083

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

0.697

9430

23986

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

0.697

9431

24073

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

0.697

9432

4

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

0.698

9433

2799

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

0.698

9434

6718

\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}

0.698

9435

9503

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

Series expansion around \(x=0\).

0.698

9436

18323

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

0.698

9437

18654

\begin{align*} x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4} \\ y^{\prime }&=\frac {x}{4}+\frac {5 y}{4} \\ \end{align*}

0.698

9438

18699

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

With initial conditions

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

0.698

9439

20838

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

0.698

9440

22327

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

0.698

9441

22623

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

0.698

9442

24019

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

0.698

9443

1359

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (6 t \right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.699

9444

1844

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

Series expansion around \(x=-1\).

0.699

9445

9592

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

Series expansion around \(x=0\).

0.699

9446

12936

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

0.699

9447

19012

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

0.699

9448

19965

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

0.699

9449

22643

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

0.699

9450

23743

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

Series expansion around \(x=0\).

0.699

9451

24638

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

0.699

9452

24768

\begin{align*} y^{\prime }-2 y-v^{\prime }-v&=6 \,{\mathrm e}^{3 x} \\ 2 y^{\prime }-3 y+v^{\prime }-3 v&=6 \,{\mathrm e}^{3 x} \\ \end{align*}

0.699

9453

26991

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

0.699

9454

26995

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

0.699

9455

1357

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (\frac {t}{4}\right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.700

9456

2044

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

Series expansion around \(x=0\).

0.700

9457

2750

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

0.700

9458

3161

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

0.700

9459

3738

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

0.700

9460

4480

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

0.700

9461

7996

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

0.700

9462

8271

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

0.700

9463

16038

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

0.700

9464

17774

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

0.700

9465

18792

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

0.700

9466

19432

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

0.700

9467

19868

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

0.700

9468

20939

\begin{align*} x^{\prime }&=4 x-13 y \\ y^{\prime }&=2 x-6 y \\ \end{align*}

With initial conditions

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

0.700

9469

21138

\begin{align*} x^{\prime \prime }-4 x^{\prime }+13 x&=20 \,{\mathrm e}^{t} \\ \end{align*}

0.700

9470

23727

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

Series expansion around \(x=0\).

0.700

9471

24576

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

0.700

9472

25595

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

0.700

9473

25762

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -11 \\ \end{align*}

0.700

9474

508

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

Series expansion around \(x=0\).

0.701

9475

3582

\begin{align*} y^{\prime }&=\frac {1}{x^{{2}/{3}}} \\ \end{align*}

0.701

9476

3736

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=169 \sin \left (3 x \right ) \\ \end{align*}

0.701

9477

7778

\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= -20 \\ \end{align*}

0.701

9478

10239

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

0.701

9479

14855

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

0.701

9480

15223

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

Using Laplace transform method.

0.701

9481

17463

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -{\frac {5}{16}} \\ y^{\prime }\left (0\right ) &= {\frac {9}{16}} \\ \end{align*}

0.701

9482

17830

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

0.701

9483

20460

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

0.701

9484

20557

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

0.701

9485

21518

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

0.701

9486

21523

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

0.701

9487

22281

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

0.701

9488

22624

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

0.701

9489

25570

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

0.701

9490

3389

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

Series expansion around \(x=0\).

0.702

9491

3907

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

0.702

9492

9510

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

Series expansion around \(x=0\).

0.702

9493

18299

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

0.702

9494

20387

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

0.702

9495

20448

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

0.702

9496

21116

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

0.702

9497

26026

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

Series expansion around \(x=0\).

0.702

9498

26195

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

0.702

9499

26747

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

With initial conditions

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

0.702

9500

3843

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

0.703