3.3.4 Problems 301 to 400

Table 3.239: Second order ode

#

ODE

Mathematica

Maple

1121

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

1122

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

1123

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 4 x^{2} \]

1124

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

1125

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

1126

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

1127

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

1128

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

1129

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

1130

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

1131

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

1132

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

1133

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

1134

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

1135

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

1136

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

1137

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

1138

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]

1139

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

1140

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

1141

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

1155

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

1156

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

1157

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {4}{1+{\mathrm e}^{-x}} \]

1158

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 3 \,{\mathrm e}^{x} \sec \left (x \right ) \]

1159

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 14 x^{\frac {3}{2}} {\mathrm e}^{x} \]

1160

\[ {}y^{\prime \prime }-y = \frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}} \]

1161

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

1162

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

1163

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

1164

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

1165

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{\frac {5}{2}} \]

1166

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

1167

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

1168

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

1169

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

1170

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

1171

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

1172

\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5} \]

1173

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

1174

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 8 x^{\frac {5}{2}} \]

1175

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

1176

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

1177

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

1178

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

1179

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

1180

\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 2 x \,{\mathrm e}^{x} \]

1181

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

1182

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

1183

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

1184

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x} \]

1185

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

1186

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

1187

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

1188

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

1189

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

1712

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

1713

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

1714

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

1715

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

1716

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

1717

\[ {}6 y^{\prime \prime }-7 y^{\prime }+y = 0 \]

1718

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

1719

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

1720

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

1721

\[ {}2 y^{\prime \prime }+y^{\prime }-10 y = 0 \]

1722

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

1723

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

1724

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

1725

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

1726

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

1727

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

1728

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

1729

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

1730

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

1731

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

1732

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

1733

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

1734

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

1735

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

1736

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

1737

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

1738

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

1739

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

1740

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

1741

\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

1742

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

1743

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

1744

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

1745

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

1746

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

1747

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

1748

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

1749

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

1750

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

1751

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

1752

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

1753

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

1754

\[ {}y^{\prime \prime }+y = \sec \left (t \right ) \]

1755

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t} \]