2.3.56 Problems 5501 to 5600

Table 2.643: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

5501

630

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

0.436

5502

1402

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

0.436

5503

3331

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

0.436

5504

4025

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

0.436

5505

5523

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

0.436

5506

9005

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

0.436

5507

11675

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

0.436

5508

14401

\begin{align*} x^{\prime }&=-5 x+3 y \\ y^{\prime }&=2 x-10 y \\ \end{align*}

0.436

5509

16768

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.436

5510

19242

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

0.436

5511

21749

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

0.436

5512

25333

\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } t -4 y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.436

5513

1629

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

0.437

5514

2013

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

0.437

5515

6390

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

0.437

5516

7831

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

0.437

5517

11214

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

0.437

5518

14881

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

0.437

5519

18919

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

0.437

5520

23580

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

0.437

5521

23595

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

0.437

5522

23828

\begin{align*} y^{\prime }&=\frac {1}{t^{2}} \\ \end{align*}

0.437

5523

25166

\begin{align*} y_{1}^{\prime }-6 y_{1}&=-4 y_{2} \\ y_{2}^{\prime }&=2 y_{1} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}

0.437

5524

983

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

0.438

5525

1025

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

0.438

5526

2718

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

0.438

5527

5417

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

0.438

5528

5511

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

0.438

5529

6477

\begin{align*} 2 y y^{\prime \prime }&=-a^{2}-4 \left (-x^{2}+b \right ) y^{2}+8 x y^{3}+3 y^{4}+{y^{\prime }}^{2} \\ \end{align*}

0.438

5530

6728

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

0.438

5531

7825

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

0.438

5532

10571

\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

0.438

5533

15945

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

0.438

5534

16827

\begin{align*} \left (1-x \right ) y^{\prime }-2 y&=0 \\ \end{align*}
Series expansion around \(x=5\).

0.438

5535

19410

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

0.438

5536

20933

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

0.438

5537

22113

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

0.438

5538

23599

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

0.438

5539

2796

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

0.439

5540

10156

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

0.439

5541

10352

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

0.439

5542

10533

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

0.439

5543

16014

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

0.439

5544

16022

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

0.439

5545

19019

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

0.439

5546

23610

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

0.439

5547

2016

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.440

5548

3951

\begin{align*} y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.440

5549

4052

\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.440

5550

4590

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

0.440

5551

14742

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

0.440

5552

20531

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

0.440

5553

23813

\begin{align*} x^{\prime }&=4 x+6 y \\ y^{\prime }&=-7 x-9 y \\ \end{align*}

0.440

5554

1376

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

0.441

5555

1790

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

0.441

5556

2427

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

0.441

5557

3233

\begin{align*} 3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y&=\frac {4}{x^{2}} \\ \end{align*}

0.441

5558

5378

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

0.441

5559

6509

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

0.441

5560

8570

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

0.441

5561

10463

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

0.441

5562

14801

\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.441

5563

15779

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

0.441

5564

17026

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

0.441

5565

18920

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

0.441

5566

19027

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

0.441

5567

19965

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

0.441

5568

20140

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

0.441

5569

22074

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

0.441

5570

23586

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

0.441

5571

612

\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}

0.442

5572

1890

\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.442

5573

3883

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

0.442

5574

7634

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

0.442

5575

16008

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

0.442

5576

16850

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

0.442

5577

18955

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.442

5578

20940

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

0.442

5579

21245

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

0.442

5580

23447

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

0.442

5581

23570

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

0.442

5582

2015

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

0.443

5583

3894

\begin{align*} x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2} \\ \end{align*}

0.443

5584

8075

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

0.443

5585

9690

\begin{align*} x^{\prime }&=12 x-9 y \\ y^{\prime }&=4 x \\ \end{align*}

0.443

5586

10259

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

0.443

5587

14803

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

N/A

N/A

N/A

0.443

5588

19667

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

0.443

5589

23774

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

0.443

5590

976

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

0.444

5591

1192

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

0.444

5592

4024

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

0.444

5593

4533

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

0.444

5594

6849

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

0.444

5595

8488

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

0.444

5596

10606

\begin{align*} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}

0.444

5597

12980

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

0.444

5598

14216

\begin{align*} Q^{\prime }&=\frac {Q}{4+Q^{2}} \\ \end{align*}

0.444

5599

14394

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

0.444

5600

18410

\begin{align*} x^{\prime }&=-9 y \\ y^{\prime }&=x \\ \end{align*}

0.444