2.3.100 Problems 9901 to 10000

Table 2.731: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9901

18284

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

0.509

9902

20425

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

0.509

9903

25703

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

0.509

9904

919

\begin{align*} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.510

9905

1898

\begin{align*} \left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}
Series expansion around \(x=1\).

0.510

9906

6148

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

0.510

9907

6416

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

0.510

9908

7642

\begin{align*} \left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 y^{\prime } x -y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.510

9909

8478

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.510

9910

9767

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

0.510

9911

9833

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

0.510

9912

10671

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

0.510

9913

14058

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

0.510

9914

14622

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

0.510

9915

16590

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{5 x} \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

0.510

9916

18235

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \\ \end{align*}

0.510

9917

18245

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

0.510

9918

18835

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.510

9919

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*}

0.510

9920

19559

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

0.510

9921

20189

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

0.510

9922

21095

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

0.510

9923

21551

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

0.510

9924

22704

\begin{align*} i^{\prime \prime }+9 i&=12 \cos \left (3 t \right ) \\ i \left (0\right ) &= 4 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.510

9925

23086

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

0.510

9926

2000

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

0.511

9927

2665

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

0.511

9928

7671

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

0.511

9929

8974

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

0.511

9930

15436

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

0.511

9931

15981

\begin{align*} x^{\prime }&=-2 x-y \\ y^{\prime }&=2 x-5 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}

0.511

9932

19629

\begin{align*} y^{\prime \prime } x +\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.511

9933

22778

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

0.511

9934

24743

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

0.511

9935

25347

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

0.511

9936

698

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

0.512

9937

1918

\begin{align*} \left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.512

9938

3484

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

0.512

9939

3982

\begin{align*} y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.512

9940

6525

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

0.512

9941

7654

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

0.512

9942

8800

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

0.512

9943

9840

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

0.512

9944

10213

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

0.512

9945

19112

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

0.512

9946

19494

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}

0.512

9947

19512

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}

0.512

9948

21137

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

0.512

9949

23091

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

0.512

9950

508

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

0.513

9951

605

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

0.513

9952

1448

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

0.513

9953

1829

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

0.513

9954

3166

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

0.513

9955

4187

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

0.513

9956

6737

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

0.513

9957

6969

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

0.513

9958

7337

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \\ \end{align*}

0.513

9959

10378

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

0.513

9960

11672

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

0.513

9961

12629

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

0.513

9962

13197

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

N/A

N/A

N/A

0.513

9963

14052

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

0.513

9964

18016

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

0.513

9965

18031

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

0.513

9966

19634

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

0.513

9967

21587

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

0.513

9968

21948

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=6 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.513

9969

21964

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

0.513

9970

23983

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

0.513

9971

916

\begin{align*} x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\ \end{align*}

0.514

9972

1343

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \\ \end{align*}

0.514

9973

1399

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

0.514

9974

3770

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

0.514

9975

10166

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

0.514

9976

13067

\begin{align*} x^{\prime }&=-5 x-2 y \\ y^{\prime }&=x-7 y \\ \end{align*}

0.514

9977

19588

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

0.514

9978

19671

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

0.514

9979

22761

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

0.514

9980

24928

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

0.514

9981

25478

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

0.514

9982

1339

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

0.515

9983

6100

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

0.515

9984

10219

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

0.515

9985

12719

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

0.515

9986

14071

\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1&=0 \\ \end{align*}

0.515

9987

18991

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

0.515

9988

1409

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

0.516

9989

2050

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

0.516

9990

2599

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

0.516

9991

2739

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

0.516

9992

5644

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

0.516

9993

6891

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

0.516

9994

9852

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

0.516

9995

12999

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

0.516

9996

14660

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

0.516

9997

14802

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\)

N/A

N/A

N/A

0.516

9998

15037

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

0.516

9999

15244

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

0.516

10000

18411

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

0.516