4.2.25 Problems 2401 to 2500

Table 4.255: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

9896

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

9897

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

9898

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

9899

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

9900

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

9912

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

9943

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

9991

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \]

9992

\[ {} y^{\prime \prime }+16 y = 4 \cos \left (x \right ) \]

9993

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

9994

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

10038

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

10039

\[ {} 5 y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]

10040

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

10041

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

10045

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

10046

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

10047

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

10048

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

10049

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

10050

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

10051

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

10052

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

10053

\[ {} y^{\prime \prime } = 1 \]

10054

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

10055

\[ {} y^{\prime \prime } = k \]

10058

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

10059

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

10063

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

10068

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

10081

\[ {} z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

10086

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

10087

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

10088

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

10091

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

10092

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

10093

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

10094

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

10095

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

10096

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

10097

\[ {} y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

10098

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

10099

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

10100

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

10101

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

10102

\[ {} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0 \]

10103

\[ {} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0 \]

10104

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

10105

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

10106

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

10107

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

10108

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

10109

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

10110

\[ {} y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0 \]

10111

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

10112

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

10113

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

10114

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

10115

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

10116

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

10117

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

10118

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

10119

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

10120

\[ {} y^{\prime \prime }-x y-x^{6}+64 = 0 \]

10121

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

10122

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

10123

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

10124

\[ {} y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0 \]

10125

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

10126

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

10127

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

10128

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

10129

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

10130

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

10131

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

10132

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

10133

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

10134

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

10135

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

10136

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

10137

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

10138

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

10139

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0 \]

10140

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0 \]

10141

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

10142

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

10143

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

10145

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

10147

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

10148

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

10149

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

10150

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

10151

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

10152

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

10153

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

10154

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

10155

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

10156

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

10157

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

10159

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