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]

1.345

8102

\begin{align*} y^{\prime \prime }&=\left (-1+x \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]]

1.422

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]]

2.292

8104

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

9.171

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]]

2.612

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]]

13.724

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)]‘]]

2.183

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]]

2.760

8109

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.290

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)]‘]]

2.606

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]]

2.479

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]]

1.812

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]]

1.620

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]]

1.609

8115

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

1.165

8116

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

Series expansion around \(x=0\).

[_linear]

0.971

8117

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

[_linear]

5.239

8118

\begin{align*} x^{3} y^{\prime \prime }+y&=\frac {1}{x^{4}} \\ \end{align*}

Series expansion around \(x=0\).

[[_2nd_order, _linear, _nonhomogeneous]]

0.279

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]]

10.527

8120

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

Series expansion around \(x=0\).

[_linear]

1.080

8121

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

Series expansion around \(x=1\).

[[_2nd_order, _missing_x]]

1.073

8122

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.311

8123

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

Series expansion around \(x=1\).

[[_Emden, _Fowler]]

1.736

8124

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.313

8125

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

Series expansion around \(x=0\).

[_separable]

0.847

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)]‘]]

1.645

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]]

1.111

8128

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.161

8129

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

Series expansion around \(x=1\).

[[_Emden, _Fowler]]

1.530

8130

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.414

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]]

1.559

8132

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.559

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]]

1.721

8134

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.543

8135

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.889

8136

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

2.172

8137

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.691

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]]

11.721

8139

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

1.178

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]]

10.051

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]]

14.016

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]]

1.155

8143

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

Series expansion around \(x=0\).

[[_2nd_order, _missing_x]]

0.944

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]]

0.458

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]]

9.980

8146

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

12.911

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]]

1.958

8148

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.553

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]]

11.455

8150

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

1.451

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]]

8.536

8152

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

[NONE]

0.038

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]]

0.049

8154

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

[NONE]

1.712

8155

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

[[_2nd_order, _missing_x]]

12.412

8156

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

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

65.387

8157

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

[[_2nd_order, _missing_x]]

42.795

8158

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

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

4.576

8159

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

[‘y=_G(x,y’)‘]

26.093

8160

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

[_separable]

18.719

8161

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

[_quadrature]

4.314

8162

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

[_quadrature]

2.946

8163

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

[[_2nd_order, _missing_x]]

0.680

8164

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.924

8165

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

[_quadrature]

0.254

8166

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

[_quadrature]

17.461

8167

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

[_separable]

24.437

8168

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

[_separable]

14.615

8169

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

[_quadrature]

5.247

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‘]]

50.122

8171

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

[_quadrature]

7.177

8172

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

[_linear]

8.658

8173

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

[[_2nd_order, _missing_x]]

0.800

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]]

0.735

8175

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

[[_linear, ‘class A‘]]

4.621

8176

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

[_linear]

6.004

8177

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

[_linear]

5.820

8178

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

[_linear]

4.594

8179

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

[_separable]

14.415

8180

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

[_separable]

26.131

8181

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

[_quadrature]

4.348

8182

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

[_quadrature]

3.723

8183

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

[[_2nd_order, _missing_x]]

0.541

8184

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

[[_2nd_order, _missing_x]]

0.562

8185

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

[[_2nd_order, _missing_y]]

1.839

8186

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

[[_Emden, _Fowler]]

0.606

8187

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

[[_Emden, _Fowler]]

6.173

8188

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

[[_3rd_order, _missing_y]]

0.566

8189

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

[_separable]

15.690

8190

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

[_quadrature]

3.497

8191

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

[_quadrature]

5.658

8192

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

[[_2nd_order, _missing_x]]

1.081

8193

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

[_quadrature]

6.395

8194

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

[_quadrature]

2.034

8195

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

[_quadrature]

10.217

8196

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

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

1.233

8197

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

system_of_ODEs

1.017

8198

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

system_of_ODEs

0.105

8199

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

[_quadrature]

19.327

8200

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.168