4.29.3 Problems 201 to 300

Table 4.1615: Second order, Linear, non-homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

8052

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

8053

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

8054

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

8056

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

8057

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

8059

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

8060

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

8162

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

8285

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

8776

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

8777

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

8778

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

8779

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

8780

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

8781

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

8782

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

8783

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

8784

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

8785

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

8786

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

8787

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

8810

\[ {} p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \]

8988

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

8990

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

8993

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

9046

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

9050

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

9197

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

9222

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

9286

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

9287

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

9288

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

9289

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

9290

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

9347

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

9648

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

9649

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

9782

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

9783

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

9795

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

10045

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

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

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

10159

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

10160

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

10161

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

10174

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

10239

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

10241

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