2.3.110 Problems 10901 to 11000

Table 2.751: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10901

17690

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

0.579

10902

3254

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

0.580

10903

4387

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

0.580

10904

5719

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

0.580

10905

6079

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

0.580

10906

8992

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

0.580

10907

14756

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

0.580

10908

16868

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

0.580

10909

17502

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

0.580

10910

20942

\begin{align*} x^{\prime }&=8 x-5 y \\ y^{\prime }&=16 x+8 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.580

10911

24948

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

0.580

10912

24965

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

0.580

10913

1996

\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.581

10914

4067

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

0.581

10915

6076

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

0.581

10916

9001

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

0.581

10917

9854

\begin{align*} \left (3 x^{2}+1\right ) y^{\prime \prime }+13 y^{\prime } x +7 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.581

10918

14301

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

0.581

10919

15833

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

0.581

10920

16391

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

0.581

10921

16907

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

0.581

10922

19059

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }&=6 x_{1}+4 x_{2}+6 x_{3} \\ x_{3}^{\prime }&=-5 x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -2 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

0.581

10923

19694

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

0.581

10924

22217

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

0.581

10925

25400

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

0.581

10926

394

\begin{align*} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\ x \left (0\right ) &= 10 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.582

10927

616

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

0.582

10928

1006

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

0.582

10929

1753

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

0.582

10930

1985

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.582

10931

4053

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

0.582

10932

5995

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

0.582

10933

6109

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

0.582

10934

7091

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

0.582

10935

7174

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

0.582

10936

9272

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

0.582

10937

12277

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

0.582

10938

14350

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

0.582

10939

15006

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

0.582

10940

16434

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

0.582

10941

16862

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

0.582

10942

16878

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

0.582

10943

17499

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

0.582

10944

17504

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \ln \left (t \right ) \\ \end{align*}

0.582

10945

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*}

0.582

10946

18854

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

0.582

10947

20675

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

0.582

10948

22212

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

0.582

10949

25807

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

0.582

10950

2279

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

0.583

10951

2803

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

0.583

10952

3550

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

0.583

10953

3820

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}

0.583

10954

4185

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

0.583

10955

4501

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

0.583

10956

8563

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

0.583

10957

12983

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

0.583

10958

14724

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

0.583

10959

16276

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

0.583

10960

16930

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

0.583

10961

17589

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

0.583

10962

19111

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

0.583

10963

25524

\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.583

10964

1022

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

0.584

10965

2660

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

0.584

10966

8416

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (-1\right ) &= -3 \\ \end{align*}

0.584

10967

9046

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

0.584

10968

9837

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+10 y^{\prime } x +20 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.584

10969

19500

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

0.584

10970

21580

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

0.584

10971

23558

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.584

10972

23755

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

0.584

10973

364

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

0.585

10974

1023

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

0.585

10975

2018

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

0.585

10976

2049

\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.585

10977

2648

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

0.585

10978

3903

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

0.585

10979

4484

\begin{align*} y^{\prime \prime }-4 y&=96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.585

10980

6574

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

0.585

10981

10240

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\ \end{align*}

0.585

10982

10421

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

0.585

10983

14051

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

0.585

10984

14365

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

0.585

10985

14836

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

0.585

10986

15396

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

0.585

10987

17329

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

0.585

10988

18441

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

0.585

10989

19043

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

0.585

10990

19497

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\ \end{align*}

0.585

10991

19630

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

0.585

10992

19760

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 y^{\prime } x&=17 x^{6} \\ \end{align*}

0.585

10993

23373

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

0.585

10994

24863

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

0.585

10995

504

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

0.586

10996

1972

\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.586

10997

1973

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

0.586

10998

1976

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

0.586

10999

1986

\begin{align*} x^{2} \left (x^{2}+8\right ) y^{\prime \prime }+7 x \left (x^{2}+2\right ) y^{\prime }-\left (-9 x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.586

11000

1999

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

0.586