4.20.51 Problems 5001 to 5100

Table 4.1299: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

24104

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

24105

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

24106

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

24107

\[ {} y^{\left (8\right )}-y = 0 \]

24108

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

24109

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

24110

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

24111

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

24112

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

24113

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

24114

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

24115

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x^{4} {\mathrm e}^{2 x} \]

24116

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

24117

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x -{\mathrm e}^{3 x} \]

24118

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

24119

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

24120

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

24121

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

24122

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

24123

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

24124

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

24129

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

24130

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 2 x \,{\mathrm e}^{3 x} \]

24131

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

24132

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

24133

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

24134

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

24135

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

24136

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

24137

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

24138

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

24139

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

24140

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

24141

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

24142

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

24143

\[ {} y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y = 4 x^{5}-6 x^{2}+2 \]

24144

\[ {} y^{\left (8\right )}+y = x^{15} \]

24145

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

24146

\[ {} y^{\prime \prime }+3 y = -x^{6}+x^{4} \]

24147

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

24148

\[ {} y^{\left (8\right )}+8 y^{\left (7\right )}+28 y^{\left (6\right )}+56 y^{\left (5\right )}+70 y^{\prime \prime \prime \prime }+56 y^{\prime \prime \prime }+28 y^{\prime \prime }+8 y^{\prime } = {\mathrm e}^{-x} x^{9} \]

24149

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = x^{2} {\mathrm e}^{x} \]

24150

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

24161

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

24162

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

24163

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

24164

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

24165

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 16 \,{\mathrm e}^{2 x} \]

24166

\[ {} y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+54 y^{\prime \prime }-108 y^{\prime }+81 y = x^{2} {\mathrm e}^{3 x} \]

24167

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

24168

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

24169

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

24170

\[ {} y^{\prime \prime }+9 y = 3 x -6 \]

24171

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

24172

\[ {} y^{\left (5\right )} = 120 \]

24174

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

24175

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

24176

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

24178

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

24179

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

24180

\[ {} y^{\left (10\right )}+y = x^{10} \]

24181

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{x}+{\mathrm e}^{2 x}+{\mathrm e}^{3 x} \]

24183

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 12 \,{\mathrm e}^{2 x} \]

24184

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

24185

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

24186

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

24187

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

24188

\[ {} y^{\prime \prime }-4 y^{\prime }-5 y = x^{2} {\mathrm e}^{-x} \]

24189

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

24190

\[ {} y^{\left (6\right )}+y = x^{7}+2 x^{3} \]

24191

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

24526

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

24527

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

24528

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

24529

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

24530

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }-15 y^{\prime } = 0 \]

24531

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

24532

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

24533

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

24534

\[ {} 4 y^{\prime \prime \prime }-13 y^{\prime }+6 y = 0 \]

24535

\[ {} 4 y^{\prime \prime \prime }-49 y^{\prime }-60 y = 0 \]

24536

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

24537

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

24538

\[ {} 10 y^{\prime \prime \prime }+y^{\prime \prime }-7 y^{\prime }+2 y = 0 \]

24539

\[ {} 4 y^{\prime \prime \prime }-13 y^{\prime }-6 y = 0 \]

24540

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

24541

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

24542

\[ {} 4 y^{\prime \prime \prime \prime }-15 y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

24543

\[ {} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-13 y^{\prime \prime }+38 y^{\prime }-24 y = 0 \]

24544

\[ {} 6 y^{\prime \prime \prime \prime }+23 y^{\prime \prime \prime }+28 y^{\prime \prime }+13 y^{\prime }+2 y = 0 \]

24545

\[ {} 4 y^{\prime \prime \prime \prime }-45 y^{\prime \prime }-70 y^{\prime }-24 y = 0 \]

24546

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

24547

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

24548

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

24549

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

24550

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

24551

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

24552

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

24553

\[ {} y^{\prime \prime }+3 y^{\prime }-10 y = 0 \]

24554

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]