3.26.10 Problems 901 to 1000

Table 3.907: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

8105

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

8106

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

8107

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

8108

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

8109

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

8110

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

8111

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

8112

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

8113

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

8114

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

8115

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

8116

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

8117

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

8118

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

8119

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

8120

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

8121

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

8122

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

8123

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

8124

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

8125

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

8126

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

8127

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

8128

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

8129

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

8130

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

8131

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

8132

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

8133

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

8134

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

8135

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

8136

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

8137

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

8138

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

8139

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \]

8140

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

8141

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

8142

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

8143

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

8144

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

8145

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

8146

\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \]

8147

\[ {}3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y = 0 \]

8148

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

8149

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

8150

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

8151

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

8152

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

8153

\[ {}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \]

8154

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

8155

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

8156

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

8157

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

8158

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

8159

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

8160

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

8161

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

8162

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

8163

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

8164

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

8165

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

8166

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

8167

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

8168

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

8169

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

8170

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

8171

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

8172

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

8173

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

8174

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

8175

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

8176

\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \]

8177

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

8178

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

8179

\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 x y}{16} = 0 \]

8180

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

8181

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

8182

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

8183

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

8184

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

8185

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

8186

\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \]

8187

\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (-2 x +1\right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \]

8188

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

8189

\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

8190

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

8191

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \]

8192

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]

8193

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

8194

\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \]

8195

\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \]

8196

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

8197

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

8198

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

8199

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

8200

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

8201

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

8202

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

8203

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

8204

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