2.2.92 Problems 9101 to 9200

Table 2.185: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

9101

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

[[_2nd_order, _linear, _nonhomogeneous]]

74.905

9102

\[ {}y^{\prime \prime }+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

1.866

9103

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

[[_2nd_order, _missing_y]]

1.880

9104

\[ {}y^{\prime \prime }+y^{\prime } = x +1 \]

[[_2nd_order, _missing_y]]

1.890

9105

\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+x +1 \]

[[_2nd_order, _missing_y]]

2.047

9106

\[ {}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \]

[[_2nd_order, _missing_y]]

2.150

9107

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

[[_2nd_order, _missing_y]]

2.352

9108

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

[[_2nd_order, _missing_y]]

2.299

9109

\[ {}y^{\prime \prime }+y = 1 \]

[[_2nd_order, _missing_x]]

2.212

9110

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

[[_2nd_order, _with_linear_symmetries]]

1.795

9111

\[ {}y^{\prime \prime }+y = x +1 \]

[[_2nd_order, _with_linear_symmetries]]

1.753

9112

\[ {}y^{\prime \prime }+y = x^{2}+x +1 \]

[[_2nd_order, _with_linear_symmetries]]

1.826

9113

\[ {}y^{\prime \prime }+y = x^{3}+x^{2}+x +1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.945

9114

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.799

9115

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.913

9116

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

[[_2nd_order, _missing_x]]

12.372

9117

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

[[_2nd_order, _missing_x]]

3.002

9118

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2.972

9119

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

[[_2nd_order, _missing_x]]

92.612

9120

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

3.010

9121

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.357

9122

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

[[_2nd_order, _missing_x]]

34.069

9123

\[ {}y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0 \]

[[_2nd_order, _missing_x]]

226.248

9124

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

[_Liouville, [_2nd_order, _reducible, _mu_xy]]

0.277

9125

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

[_Liouville, [_2nd_order, _reducible, _mu_xy]]

0.436

9126

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

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.116

9127

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

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.716

9128

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

4.720

9129

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

4.220

9130

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

[[_homogeneous, ‘class C‘], _dAlembert]

172.091

9131

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

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.124

9132

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

[_Liouville, [_2nd_order, _reducible, _mu_xy]]

0.341

9133

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

[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

0.835

9134

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

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.679

9135

\[ {}10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0 \]

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.245

9136

\[ {}10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0 \]

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.987

9137

\[ {}y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.031

9138

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.568

9139

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

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

1.093

9140

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

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

1.811

9141

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4.045

9142

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

[[_2nd_order, _with_linear_symmetries]]

1.707

9143

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

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

1.662

9144

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.517

9145

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

[[_2nd_order, _with_linear_symmetries]]

3.261

9146

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

29.319

9147

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.163

9148

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.727

9149

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.664

9150

\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x^{m +1} \]

[[_2nd_order, _with_linear_symmetries]]

1.968

9151

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

[[_2nd_order, _with_linear_symmetries]]

1.062

9152

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

[_Lienard]

4.782

9153

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.648

9154

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

[[_2nd_order, _linear, _nonhomogeneous]]

49.800

9155

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.931

9156

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

51.144

9157

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

[[_2nd_order, _with_linear_symmetries]]

2.847

9158

\[ {}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.342

9159

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

[[_2nd_order, _with_linear_symmetries]]

0.127

9160

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

[[_2nd_order, _with_linear_symmetries]]

1.017

9161

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

[_Lienard]

1.336

9162

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

[_linear]

1.929

9163

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

[_rational]

1.463

9164

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

[[_Riccati, _special]]

1.002

9165

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \]

[[_high_order, _linear, _nonhomogeneous]]

0.176

9166

\[ {}x^{2} y^{\prime \prime }-x \left (x +6\right ) y^{\prime }+10 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.342

9167

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

[_Bessel]

0.648

9168

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

[_Bessel]

0.900

9169

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

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

0.880

9170

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

[[_3rd_order, _with_linear_symmetries]]

0.036

9171

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

2.208

9172

\[ {}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=y-x \end {array}\right ] \]

system_of_ODEs

0.423

9173

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

[_Gegenbauer]

0.228

9174

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

0.231

9175

\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.442

9176

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

[_Gegenbauer]

0.210

9177

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

[[_2nd_order, _with_linear_symmetries]]

0.307

9178

\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.339

9179

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

[[_2nd_order, _with_linear_symmetries]]

0.339

9180

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

[[_2nd_order, _with_linear_symmetries]]

0.306

9181

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

[[_2nd_order, _with_linear_symmetries]]

0.238

9182

\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.374

9183

\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.299

9184

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

[[_2nd_order, _with_linear_symmetries]]

0.410

9185

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

[[_2nd_order, _with_linear_symmetries]]

0.108

9186

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

[_Laguerre]

0.241

9187

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

[[_2nd_order, _with_linear_symmetries]]

0.259

9188

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

[[_2nd_order, _with_linear_symmetries]]

0.173

9189

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

[_Laguerre]

0.305

9190

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

[[_2nd_order, _with_linear_symmetries]]

0.320

9191

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

[[_2nd_order, _with_linear_symmetries]]

0.242

9192

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

[[_2nd_order, _with_linear_symmetries]]

0.351

9193

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

[[_2nd_order, _with_linear_symmetries]]

0.314

9194

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

[[_2nd_order, _with_linear_symmetries]]

0.322

9195

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

[[_2nd_order, _with_linear_symmetries]]

0.241

9196

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

[[_2nd_order, _with_linear_symmetries]]

0.320

9197

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

[[_2nd_order, _with_linear_symmetries]]

0.241

9198

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

[[_2nd_order, _with_linear_symmetries]]

1.105

9199

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.118

9200

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

[[_2nd_order, _with_linear_symmetries]]

0.316