2.2.82 Problems 8101 to 8200

Table 2.181: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

8101

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Series expansion around \(x=0\).

[_Gegenbauer]

0.376

8102

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

[[_2nd_order, _with_linear_symmetries]]

0.317

8103

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

[[_2nd_order, _with_linear_symmetries]]

1.618

8104

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

[[_Emden, _Fowler]]

3.200

8105

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

[[_2nd_order, _with_linear_symmetries]]

0.445

8106

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

[[_2nd_order, _exact, _linear, _homogeneous]]

3.821

8107

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

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

1.564

8108

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

[[_2nd_order, _with_linear_symmetries]]

1.927

8109

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

[[_Emden, _Fowler]]

0.257

8110

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

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

1.801

8111

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.738

8112

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

[[_2nd_order, _with_linear_symmetries]]

0.521

8113

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

[[_2nd_order, _with_linear_symmetries]]

0.512

8114

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {25}{4}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.515

8115

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

[[_2nd_order, _with_linear_symmetries]]

0.296

8116

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

[_linear]

0.450

8117

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

[_linear]

3.671

8118

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.070

8119

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.471

8120

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

[_linear]

0.249

8121

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

[[_2nd_order, _missing_x]]

0.300

8122

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

[[_Emden, _Fowler]]

0.266

8123

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

[[_Emden, _Fowler]]

0.377

8124

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

[[_Emden, _Fowler]]

0.245

8125

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

[_separable]

0.364

8126

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

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

0.496

8127

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

[[_2nd_order, _with_linear_symmetries]]

0.254

8128

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

[[_Emden, _Fowler]]

0.332

8129

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

[[_Emden, _Fowler]]

0.419

8130

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

[[_Emden, _Fowler]]

0.277

8131

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.375

8132

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

[[_Emden, _Fowler]]

1.525

8133

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

[[_2nd_order, _with_linear_symmetries]]

1.579

8134

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

[[_Emden, _Fowler]]

1.518

8135

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

[[_Emden, _Fowler]]

0.484

8136

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

[[_Emden, _Fowler]]

1.563

8137

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

[[_Emden, _Fowler]]

1.553

8138

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

[[_2nd_order, _with_linear_symmetries]]

3.699

8139

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

[[_2nd_order, _with_linear_symmetries]]

0.157

8140

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

[[_2nd_order, _with_linear_symmetries]]

3.393

8141

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

[[_2nd_order, _with_linear_symmetries]]

4.279

8142

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

[[_2nd_order, _missing_x]]

0.284

8143

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

[[_2nd_order, _missing_x]]

0.244

8144

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

[[_2nd_order, _with_linear_symmetries]]

0.090

8145

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

[[_2nd_order, _with_linear_symmetries]]

3.412

8146

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

[[_2nd_order, _with_linear_symmetries]]

4.151

8147

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

[[_2nd_order, _with_linear_symmetries]]

0.649

8148

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

[[_Emden, _Fowler]]

1.528

8149

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

[[_2nd_order, _with_linear_symmetries]]

3.623

8150

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

[[_Emden, _Fowler]]

0.495

8151

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

[[_2nd_order, _linear, _nonhomogeneous]]

10.987

8152

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

[NONE]

0.031

8153

\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.042

8154

\begin{align*} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\ \end{align*}

[NONE]

1.311

8155

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

[[_2nd_order, _missing_x]]

3.491

8156

\begin{align*} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align*}

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

112.160

8157

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

[[_2nd_order, _missing_x]]

41.012

8158

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

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

2.511

8159

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

[‘y=_G(x,y’)‘]

25.211

8160

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

[_separable]

11.231

8161

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

[_quadrature]

2.148

8162

\begin{align*} y^{\prime }+20 y&=24 \\ \end{align*}

[_quadrature]

2.016

8163

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.325

8164

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.651

8165

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

[_quadrature]

0.193

8166

\begin{align*} y^{\prime }&=25+y^{2} \\ \end{align*}

[_quadrature]

10.131

8167

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

[_separable]

11.540

8168

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

[_separable]

10.864

8169

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

[_quadrature]

2.087

8170

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

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17.659

8171

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

[_quadrature]

3.515

8172

\begin{align*} y^{\prime }+4 y x&=8 x^{3} \\ \end{align*}

[_linear]

7.879

8173

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

[[_2nd_order, _missing_x]]

0.322

8174

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.305

8175

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

[[_linear, ‘class A‘]]

3.766

8176

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

[_linear]

5.342

8177

\begin{align*} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\ \end{align*}

[_linear]

5.398

8178

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

[_linear]

3.685

8179

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

[_separable]

9.864

8180

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

[_separable]

15.081

8181

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

[_quadrature]

3.327

8182

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

[_quadrature]

2.219

8183

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.256

8184

\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.273

8185

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

[[_2nd_order, _missing_y]]

1.811

8186

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

[[_Emden, _Fowler]]

0.327

8187

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

2.369

8188

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

[[_3rd_order, _missing_y]]

0.259

8189

\begin{align*} 3 y^{\prime } x +5 y&=10 \\ \end{align*}

[_separable]

11.227

8190

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

[_quadrature]

2.145

8191

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

[_quadrature]

2.334

8192

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.466

8193

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

[_quadrature]

2.265

8194

\begin{align*} {y^{\prime }}^{2}&=9-y^{2} \\ \end{align*}

[_quadrature]

0.969

8195

\begin{align*} y y^{\prime }+\sqrt {16-y^{2}}&=0 \\ \end{align*}

[_quadrature]

3.041

8196

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

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

0.536

8197

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

system_of_ODEs

0.372

8198

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

system_of_ODEs

0.031

8199

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

[_quadrature]

5.791

8200

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.514