6.82 Problems 8101 to 8200

Table 6.163: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

8101

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

8102

\[ {} x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \]

8103

\[ {} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \]

8104

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

8105

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

8106

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

8107

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

8108

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

8109

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

8110

\[ {} y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

8111

\[ {} y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

8112

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

8113

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

8114

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

8115

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

8116

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

8117

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

8118

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

8119

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

8120

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

8121

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

8122

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

8123

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

8124

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y = 0 \]

8125

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

8126

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

8127

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

8128

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

8129

\[ {} x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}} \]

8130

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

8131

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

8132

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

8133

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

8134

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

8135

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

8136

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

8137

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

8138

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

8139

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

8140

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

8141

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

8142

\[ {} y^{\prime \prime }-x y = \frac {1}{1-x} \]

8143

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

8144

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

8145

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

8146

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

8147

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

8148

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

8149

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

8150

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

8151

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

8152

\[ {} x y^{\prime \prime }+x y^{\prime }-y \,{\mathrm e}^{x} = 0 \]

8153

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

8154

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

8155

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

8156

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

8157

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

8158

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

8159

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

8160

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

8161

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

8162

\[ {} \left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y = \cos \left (x \right ) \]

8163

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

8164

\[ {} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0 \]

8165

\[ {} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right ) \]

8166

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

8167

\[ {} R^{\prime \prime } = -\frac {k}{R^{2}} \]

8168

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

8169

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

8170

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

8171

\[ {} y^{2}-1+x y^{\prime } = 0 \]

8172

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

8173

\[ {} y^{\prime }+20 y = 24 \]

8174

\[ {} y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

8175

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

8176

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

8177

\[ {} y^{\prime } = 25+y^{2} \]

8178

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

8179

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

8180

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

8181

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

8182

\[ {} p^{\prime } = p \left (1-p\right ) \]

8183

\[ {} y^{\prime }+4 x y = 8 x^{3} \]

8184

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

8185

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 12 x^{2} \]

8186

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

8187

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

8188

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

8189

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

8190

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

8191

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

8192

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

8193

\[ {} 5 y^{\prime } = 2 y \]

8194

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 0 \]

8195

\[ {} 2 y^{\prime \prime }+7 y^{\prime }-4 y = 0 \]

8196

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

8197

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

8198

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

8199

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

8200

\[ {} 3 x y^{\prime }+5 y = 10 \]