2.62 Problems 6101 to 6200

Table 2.62: Main lookup table

#

ODE

Mathematica result

Maple result

6101

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

6102

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

6103

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

6104

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

6105

\[ {}\left (y^{\prime \prime }\right )^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]

6106

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

6107

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

6108

\[ {}y^{\prime \prime }+y = -\cos \relax (x ) \]

6109

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \]

6110

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

6111

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

6112

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

6113

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

6114

\[ {}9 \left (y^{\prime }\right )^{2}+3 x y^{4} y^{\prime }+y^{5} = 0 \]

6115

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

6116

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

6117

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

6118

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

6119

\[ {}4 x^{5} \left (y^{\prime }\right )^{2}+12 x^{4} y y^{\prime }+9 = 0 \]

6120

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

6121

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

6122

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

6123

\[ {}16 x \left (y^{\prime }\right )^{2}+8 y y^{\prime }+y^{6} = 0 \]

6124

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

6125

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

6126

\[ {}9 x y^{4} \left (y^{\prime }\right )^{2}-3 y^{5} y^{\prime }-1 = 0 \]

6127

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

6128

\[ {}x^{6} \left (y^{\prime }\right )^{2} = 16 y+8 x y^{\prime } \]

6129

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

6130

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

6131

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

6132

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

6133

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

6134

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

6135

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

6136

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

6137

\[ {}y^{\prime \prime }-9 y = 0 \]

6138

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

6139

\[ {}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0 \]

6140

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y = 0 \]

6141

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

6142

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y = 0 \]

6143

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

6144

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

6145

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

6146

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

6147

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+3 y = 0 \]

6148

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

6149

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

6150

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

6151

\[ {}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

6152

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

6153

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

6154

\[ {}y^{\prime \prime }+3 x y^{\prime }+7 y = 0 \]

6155

\[ {}2 y^{\prime \prime }+9 x y^{\prime }-36 y = 0 \]

6156

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

6157

\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]

6158

\[ {}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0 \]

6159

\[ {}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y = 0 \]

6160

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 x y^{\prime }+9 y = 0 \]

6161

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

6162

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

6163

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

6164

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

6165

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

6166

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

6167

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

6168

\[ {}2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y = 0 \]

6169

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

6170

\[ {}8 x^{2} y^{\prime \prime }+10 x y^{\prime }-\left (x +1\right ) y = 0 \]

6171

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

6172

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

6173

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

6174

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

6175

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

6176

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

6177

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

6178

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

6179

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

6180

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

6181

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

6182

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

6183

\[ {}9 x^{2} y^{\prime \prime }+2 y = 0 \]

6184

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

6185

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

6186

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

6187

\[ {}9 x^{2} y^{\prime \prime }+2 y = 0 \]

6188

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

6189

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

6190

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

6191

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

6192

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

6193

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

6194

\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \]

6195

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

6196

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

6197

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

6198

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

6199

\[ {}x \left (x +1\right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0 \]

6200

\[ {}x^{2} y^{\prime \prime }-x \left (3 x +1\right ) y^{\prime }+\left (1-6 x \right ) y = 0 \]