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

14547

\begin{align*} 8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

1.166

9902

18119

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

1.166

9903

24994

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

1.166

9904

9547

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

1.167

9905

9760

\begin{align*} 5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}

1.168

9906

19009

\begin{align*} x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=-x_{2}-x_{3} \\ \end{align*}

1.168

9907

20474

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

1.168

9908

25362

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

1.168

9909

8250

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

1.169

9910

7428

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

1.171

9911

9894

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

1.171

9912

23964

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

1.171

9913

2094

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

1.172

9914

5411

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

1.172

9915

9545

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

1.172

9916

9398

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

1.173

9917

18954

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

1.173

9918

16233

\begin{align*} y^{\prime }&=200 y-2 y^{2} \\ \end{align*}

1.174

9919

18246

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

1.174

9920

2363

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

1.175

9921

16158

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

1.175

9922

5753

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

1.176

9923

7096

\begin{align*} y^{\prime \prime }+9 y&=8 \cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

1.176

9924

15113

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

1.176

9925

23619

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

1.176

9926

25532

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

1.176

9927

1095

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

1.177

9928

6878

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

1.177

9929

10736

\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}

1.177

9930

23154

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

1.177

9931

4059

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

1.178

9932

2662

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

1.179

9933

10360

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

1.179

9934

1106

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

1.180

9935

4575

\begin{align*} x_{1}^{\prime }&=-x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \\ \end{align*}

1.180

9936

15280

\begin{align*} x^{\prime }&=-7 x+6 y+6 \,{\mathrm e}^{-t} \\ y^{\prime }&=-12 x+5 y+37 \\ \end{align*}

1.180

9937

15550

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

1.180

9938

1495

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.181

9939

9868

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

1.181

9940

19478

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

1.181

9941

21431

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

1.181

9942

21561

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

1.181

9943

22739

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

1.181

9944

125

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

1.182

9945

23301

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

1.182

9946

25473

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

1.182

9947

2355

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

1.183

9948

19134

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

1.183

9949

24823

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

1.183

9950

664

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

1.184

9951

3888

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=6 x_{2}-7 x_{3}+3 x_{4} \\ x_{3}^{\prime }&=3 x_{3}-x_{4} \\ x_{4}^{\prime }&=-4 x_{2}+9 x_{3}-3 x_{4} \\ \end{align*}

1.184

9952

8910

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

1.184

9953

9394

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

1.184

9954

18019

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

1.184

9955

18730

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

1.184

9956

20436

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

1.184

9957

21566

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

1.184

9958

17098

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

1.185

9959

4268

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

1.186

9960

23136

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

1.186

9961

2214

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \\ \end{align*}

1.187

9962

3399

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

1.187

9963

4039

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

1.187

9964

5489

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

1.187

9965

8286

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

1.187

9966

10615

\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}

1.187

9967

14249

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

1.187

9968

23193

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

1.187

9969

24814

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

1.187

9970

1260

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

1.188

9971

7227

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

1.188

9972

7596

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

1.188

9973

10486

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

1.188

9974

24850

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

1.188

9975

23620

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

1.189

9976

25698

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

1.189

9977

4580

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

1.190

9978

25234

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

1.190

9979

2096

\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.191

9980

7594

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -12 \\ \end{align*}

1.191

9981

9397

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

1.191

9982

18940

\begin{align*} y^{\prime \prime }-y&=-20 \delta \left (t -3\right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

1.192

9983

2091

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

1.193

9984

5649

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

1.193

9985

8899

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

1.193

9986

2098

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

1.194

9987

4579

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}

1.194

9988

20133

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

1.194

9989

24813

\begin{align*} x^{6} {y^{\prime }}^{3}-3 y^{\prime } x -3 y&=0 \\ \end{align*}

1.194

9990

2302

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

1.195

9991

10738

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

1.195

9992

24819

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

1.195

9993

25001

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

1.195

9994

9897

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

1.196

9995

12875

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

1.196

9996

17726

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

1.196

9997

25290

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

1.196

9998

994

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 3 \\ \end{align*}

1.197

9999

18998

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

1.197

10000

6708

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

1.198