2.2.100 Problems 9901 to 10000

Table 2.201: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

9901

\[ {}y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.184

9902

\[ {}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.588

9903

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.237

9904

\[ {}2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.193

9905

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.220

9906

\[ {}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.189

9907

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

0.363

9908

\[ {}x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.309

9909

\[ {}x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.237

9910

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.316

9911

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.360

9912

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.445

9913

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.437

9914

\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \]

[_Hermite]

0.328

9915

\[ {}\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.338

9916

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \]

[[_Emden, _Fowler]]

0.310

9917

\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.460

9918

\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.315

9919

\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.448

9920

\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \]

[[_Emden, _Fowler]]

0.232

9921

\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \]

[_Laguerre]

0.431

9922

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.300

9923

\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.091

9924

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.172

9925

\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.353

9926

\[ {}x^{4} y^{\prime \prime }+\lambda y = 0 \]

[[_Emden, _Fowler]]

0.329

9927

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.393

9928

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.189

9929

\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.359

9930

\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \]

[[_Emden, _Fowler]]

0.361

9931

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.163

9932

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.375

9933

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.417

9934

\[ {}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0 \]

[_Laguerre]

0.255

9935

\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.307

9936

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

0.337

9937

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.089

9938

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]

[_Gegenbauer]

0.381

9939

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

0.156

9940

\[ {}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.181

9941

\[ {}2 x \left (-1+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Jacobi]

0.217

9942

\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.171

9943

\[ {}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.097

9944

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.180

9945

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.179

9946

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \]

[_Jacobi]

0.352

9947

\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.345

9948

\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.341

9949

\[ {}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.363

9950

\[ {}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.226

9951

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.191

9952

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.184

9953

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

0.243

9954

\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler]]

0.367

9955

\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.300

9956

\[ {}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.247

9957

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

0.157

9958

\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.126

9959

\[ {}u^{\prime \prime }+2 u^{\prime }+u = 0 \]

[[_2nd_order, _missing_x]]

0.247

9960

\[ {}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.109

9961

\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (3 x +1\right )^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.163

9962

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.162

9963

\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.148

9964

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.322

9965

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.318

9966

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.325

9967

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.260

9968

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.321

9969

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.317

9970

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.325

9971

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.317

9972

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.317

9973

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.323

9974

\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.324

9975

\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \]

[_Lienard]

0.154

9976

\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0 \]

[[_Emden, _Fowler]]

0.202

9977

\[ {}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.302

9978

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.210

9979

\[ {}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.348

9980

\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.392

9981

\[ {}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.233

9982

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.162

9983

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.172

9984

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.329

9985

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.172

9986

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0 \]

[[_Emden, _Fowler]]

0.367

9987

\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

0.293

9988

\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.102

9989

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.173

9990

\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.123

9991

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

0.209

9992

\[ {}y^{\prime \prime } = \frac {2 y}{x^{2}} \]

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.125

9993

\[ {}y^{\prime \prime } = \frac {6 y}{x^{2}} \]

[[_Emden, _Fowler]]

0.128

9994

\[ {}y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (-1+x \right )^{2}}+\frac {3}{16 x \left (-1+x \right )}\right ) y \]

[[_2nd_order, _with_linear_symmetries]]

1.132

9995

\[ {}y^{\prime \prime } = \frac {20 y}{x^{2}} \]

[[_Emden, _Fowler]]

0.126

9996

\[ {}y^{\prime \prime } = \frac {12 y}{x^{2}} \]

[[_Emden, _Fowler]]

0.124

9997

\[ {}y^{\prime \prime }-\frac {y}{4 x^{2}} = 0 \]

[[_Emden, _Fowler]]

0.227

9998

\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.158

9999

\[ {}y^{\prime \prime }+\frac {y}{x^{2}} = 0 \]

[[_Emden, _Fowler]]

0.323

10000

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.769