2.3.97 Problems 9601 to 9700

Table 2.725: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9601

20163

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

0.489

9602

20552

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

0.489

9603

22786

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

0.489

9604

24071

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

0.489

9605

1903

\begin{align*} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}
Series expansion around \(x=1\).

0.490

9606

2057

\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.490

9607

5441

\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}

0.490

9608

5822

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

0.490

9609

7779

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

0.490

9610

10443

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

0.490

9611

14801

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

N/A

N/A

N/A

0.490

9612

16094

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

0.490

9613

18099

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

0.490

9614

18332

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

0.490

9615

18894

\begin{align*} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 9 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.490

9616

19552

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

0.490

9617

20366

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

0.490

9618

22693

\begin{align*} s^{\prime \prime }-3 s^{\prime }+2 s&=8 t^{2}+12 \,{\mathrm e}^{-t} \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.490

9619

23556

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

0.490

9620

25195

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

0.490

9621

1342

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

0.491

9622

4023

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

0.491

9623

9383

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

0.491

9624

16691

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

0.491

9625

16883

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

0.491

9626

17807

\begin{align*} \frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.491

9627

18323

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

0.491

9628

19556

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \,{\mathrm e}^{5 x} \\ \end{align*}

0.491

9629

20855

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

0.491

9630

22941

\begin{align*} x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\ -x+y^{\prime }-y&=0 \\ \end{align*}

0.491

9631

24908

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

0.491

9632

25276

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}+1} \\ \end{align*}

0.491

9633

462

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

0.492

9634

883

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \\ \end{align*}

0.492

9635

13152

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

N/A

N/A

N/A

0.492

9636

16430

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

0.492

9637

17407

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

0.492

9638

18677

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

0.492

9639

21915

\begin{align*} y^{\prime \prime }+9 y&=5 \cos \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.492

9640

23449

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

0.492

9641

25129

\begin{align*} y^{\prime \prime }+y&=10 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.492

9642

2619

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

0.493

9643

3114

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

0.493

9644

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*}

0.493

9645

7372

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

0.493

9646

9324

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

0.493

9647

9425

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

0.493

9648

9571

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \\ \end{align*}

0.493

9649

10838

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

0.493

9650

14678

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

0.493

9651

15275

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

0.493

9652

15389

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

0.493

9653

16087

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.493

9654

16870

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

0.493

9655

17720

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

0.493

9656

18931

\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}
Using Laplace transform method.

0.493

9657

19462

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

0.493

9658

25369

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

0.493

9659

881

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

0.494

9660

914

\begin{align*} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\ \end{align*}

0.494

9661

1508

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}
Using Laplace transform method.

0.494

9662

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*}

0.494

9663

5631

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

0.494

9664

5790

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

0.494

9665

8614

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.494

9666

9694

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

0.494

9667

9834

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

0.494

9668

9850

\begin{align*} 2 y^{\prime \prime }+9 y^{\prime } x -36 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.494

9669

10527

\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}

0.494

9670

14807

\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.494

9671

15184

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

0.494

9672

16851

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

0.494

9673

21628

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

0.494

9674

21666

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

0.494

9675

21855

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

0.494

9676

22870

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.494

9677

24868

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

0.494

9678

1899

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y&=0 \\ y \left (-1\right ) &= 1 \\ y^{\prime }\left (-1\right ) &= -1 \\ \end{align*}
Series expansion around \(x=-1\).

0.495

9679

15160

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

0.495

9680

21165

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

0.495

9681

21649

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

0.495

9682

22312

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

0.495

9683

23578

\begin{align*} N_{1}^{\prime }&=4 N_{1}-6 N_{2} \\ N_{2}^{\prime }&=8 N_{1}-10 N_{2} \\ \end{align*}
With initial conditions
\begin{align*} N_{1} \left (0\right ) &= 100000 \\ N_{2} \left (0\right ) &= 1000 \\ \end{align*}

0.495

9684

25577

\begin{align*} m y^{\prime \prime }+k y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.495

9685

63

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

0.496

9686

2055

\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*}
Series expansion around \(x=0\).

0.496

9687

2060

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

0.496

9688

8890

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

0.496

9689

13189

\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.496

9690

15581

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

0.496

9691

17459

\begin{align*} y^{\prime \prime }-4 y&=32 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.496

9692

18326

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

0.496

9693

18678

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

0.496

9694

20530

\begin{align*} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}

0.496

9695

20616

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

0.496

9696

22192

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

0.496

9697

344

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

0.497

9698

1020

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

0.497

9699

4044

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

0.497

9700

4413

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

0.497