2.3.100 Problems 9901 to 10000

Table 2.743: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9901

14684

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

0.675

9902

17590

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

0.675

9903

22845

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

0.675

9904

24759

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

0.675

9905

3838

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=5 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=2 x_{2}-4 x_{3} \\ \end{align*}

0.676

9906

6212

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

0.676

9907

9852

\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+3 y^{\prime } x -8 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.676

9908

10358

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

0.676

9909

10519

\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}

0.676

9910

12891

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

0.676

9911

15396

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

0.676

9912

17515

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

0.676

9913

502

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

0.677

9914

3504

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

0.677

9915

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 \(x=0\).

0.677

9916

4504

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=15 \,{\mathrm e}^{-x} \sqrt {x +1} \\ \end{align*}

0.677

9917

8108

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

0.677

9918

8219

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

0.677

9919

8590

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

0.677

9920

10291

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

0.677

9921

11723

\begin{align*} y^{\prime }-1&=0 \\ \end{align*}

0.677

9922

16121

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

0.677

9923

18238

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

0.677

9924

18645

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

0.677

9925

18989

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

0.677

9926

19051

\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*}

0.677

9927

7768

\begin{align*} y^{\prime \prime }-y^{\prime }+10 y&=20-{\mathrm e}^{2 x} \\ \end{align*}

0.678

9928

7959

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

0.678

9929

8599

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

0.678

9930

10359

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

0.678

9931

17522

\begin{align*} y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.678

9932

22827

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

0.678

9933

25192

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

0.678

9934

26063

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

0.678

9935

5390

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

0.679

9936

6051

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

0.679

9937

9375

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

0.679

9938

9851

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

0.679

9939

9856

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

0.679

9940

11773

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

0.679

9941

16039

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

0.679

9942

16596

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \\ \end{align*}

0.679

9943

20985

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

0.679

9944

21891

\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}

0.679

9945

23037

\begin{align*} y^{\prime \prime }+3 y^{\prime }+5 y&=4 \,{\mathrm e}^{3 t} \\ \end{align*}

0.679

9946

23588

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

0.679

9947

2753

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

0.680

9948

3363

\begin{align*} 2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.680

9949

3972

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

0.680

9950

8518

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

0.680

9951

13771

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

0.680

9952

23457

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

0.680

9953

23758

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

0.680

9954

24757

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

0.680

9955

5402

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

0.681

9956

8617

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

0.681

9957

9702

\begin{align*} x^{\prime }&=4 x+5 y \\ y^{\prime }&=-2 x+6 y \\ \end{align*}

0.681

9958

9844

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

0.681

9959

10217

\begin{align*} x^{2} y^{\prime \prime }-9 y^{\prime } x +25 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.681

9960

10297

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

0.681

9961

12668

\begin{align*} y^{\prime \prime }&=\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (a \,x^{4}+10 x^{2}+1\right ) y}{4 x^{6}} \\ \end{align*}

0.681

9962

14406

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

0.681

9963

15278

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

0.681

9964

15493

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

0.681

9965

16060

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

0.681

9966

17696

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

0.681

9967

17767

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

0.681

9968

19210

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

0.681

9969

19883

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

0.681

9970

22690

\begin{align*} 4 i^{\prime \prime }+i&=t^{2}+2 \cos \left (4 t \right ) \\ \end{align*}

0.681

9971

5934

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

0.682

9972

10231

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

0.682

9973

14385

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

0.682

9974

14814

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.682

9975

20622

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

0.682

9976

23500

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

0.682

9977

23666

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

0.682

9978

11

\begin{align*} x^{\prime \prime }&=50 \\ x \left (0\right ) &= 20 \\ x^{\prime }\left (0\right ) &= 10 \\ \end{align*}

0.683

9979

825

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

0.683

9980

846

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

0.683

9981

1762

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

0.683

9982

6518

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

0.683

9983

7102

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

0.683

9984

9588

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

0.683

9985

17002

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

0.683

9986

17868

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

0.683

9987

20379

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 \cos \left (x \right ) x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 12 \\ \end{align*}

0.683

9988

21751

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

0.683

9989

22829

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

0.683

9990

3367

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

0.684

9991

3761

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \\ \end{align*}

0.684

9992

3887

\begin{align*} x_{1}^{\prime }&=-8 x_{1}+6 x_{2}-3 x_{3} \\ x_{2}^{\prime }&=-12 x_{1}+10 x_{2}-3 x_{3} \\ x_{3}^{\prime }&=-2 x_{3} \\ \end{align*}

0.684

9993

10345

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

0.684

9994

10944

\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*}

0.684

9995

11753

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

0.684

9996

14377

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

0.684

9997

15688

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \\ \end{align*}

0.684

9998

16092

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=-8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.684

9999

18632

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

0.684

10000

18851

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

0.684