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 x y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

Series expansion around \(x=0\).

[_Gegenbauer]

0.471

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]]

0.395

8103

\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 \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.852

8104

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

2.225

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]]

0.552

8106

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

Series expansion around \(x=0\).

[[_2nd_order, _exact, _linear, _homogeneous]]

3.257

8107

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

Series expansion around \(x=0\).

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

0.772

8108

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

1.147

8109

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.336

8110

\begin{align*} x \left (x +2\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)]‘]]

1.041

8111

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

Series expansion around \(x=0\).

[[_2nd_order, _exact, _linear, _homogeneous]]

0.954

8112

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.645

8113

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.638

8114

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.613

8115

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.381

8116

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

Series expansion around \(x=0\).

[_linear]

0.474

8117

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

[_linear]

1.948

8118

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

Series expansion around \(x=0\).

[[_2nd_order, _linear, _nonhomogeneous]]

0.089

8119

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

Series expansion around \(x=0\).

[[_2nd_order, _linear, _nonhomogeneous]]

2.513

8120

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

Series expansion around \(x=0\).

[_linear]

0.279

8121

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

Series expansion around \(x=1\).

[[_2nd_order, _missing_x]]

0.368

8122

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.352

8123

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

Series expansion around \(x=1\).

[[_Emden, _Fowler]]

0.477

8124

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.327

8125

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

Series expansion around \(x=0\).

[_separable]

0.366

8126

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

Series expansion around \(x=0\).

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

0.614

8127

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.332

8128

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.392

8129

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

Series expansion around \(x=1\).

[[_Emden, _Fowler]]

0.532

8130

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.353

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]]

0.447

8132

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.634

8133

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.691

8134

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.622

8135

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.648

8136

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.757

8137

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.661

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]]

2.931

8139

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.257

8140

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

2.461

8141

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

3.788

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]]

0.365

8143

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

Series expansion around \(x=0\).

[[_2nd_order, _missing_x]]

0.311

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]]

0.137

8145

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

2.451

8146

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

3.420

8147

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

Series expansion around \(x=0\).

[[_2nd_order, _with_linear_symmetries]]

0.779

8148

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.622

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]]

2.802

8150

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

Series expansion around \(x=0\).

[[_Emden, _Fowler]]

0.547

8151

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

[[_2nd_order, _linear, _nonhomogeneous]]

9.013

8152

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

[NONE]

0.036

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]]

0.045

8154

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

[NONE]

1.655

8155

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

[[_2nd_order, _missing_x]]

3.960

8156

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

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

46.433

8157

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

[[_2nd_order, _missing_x]]

42.875

8158

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

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

1.864

8159

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

[‘y=_G(x,y’)‘]

25.509

8160

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

[_separable]

5.703

8161

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

[_quadrature]

1.378

8162

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

[_quadrature]

1.100

8163

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

[[_2nd_order, _missing_x]]

0.398

8164

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.636

8165

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

[_quadrature]

0.201

8166

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

[_quadrature]

8.641

8167

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

[_separable]

6.560

8168

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

[_separable]

5.395

8169

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

[_quadrature]

1.437

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‘]]

11.932

8171

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

[_quadrature]

1.929

8172

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

[_linear]

3.168

8173

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

[[_2nd_order, _missing_x]]

0.418

8174

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.408

8175

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

[[_linear, ‘class A‘]]

1.842

8176

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

[_linear]

2.415

8177

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

[_linear]

2.456

8178

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

[_linear]

1.758

8179

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

[_separable]

4.468

8180

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

[_separable]

7.448

8181

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

[_quadrature]

1.413

8182

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

[_quadrature]

1.233

8183

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

[[_2nd_order, _missing_x]]

0.293

8184

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

[[_2nd_order, _missing_x]]

0.309

8185

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

[[_2nd_order, _missing_y]]

0.849

8186

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

[[_Emden, _Fowler]]

0.364

8187

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

[[_Emden, _Fowler]]

1.905

8188

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

[[_3rd_order, _missing_y]]

0.294

8189

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

[_separable]

4.934

8190

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

[_quadrature]

1.055

8191

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

[_quadrature]

1.602

8192

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

[[_2nd_order, _missing_x]]

0.559

8193

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

[_quadrature]

1.572

8194

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

[_quadrature]

1.002

8195

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

[_quadrature]

2.310

8196

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

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

0.587

8197

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

system_of_ODEs

0.474

8198

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

system_of_ODEs

0.039

8199

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

[_quadrature]

4.489

8200

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.584