4.3.85 Problems 8401 to 8500

Table 4.533: Second order ode

#

ODE

Mathematica

Maple

Sympy

24096

\[ {} y^{\prime \prime }+\frac {327 y^{\prime }}{100}-\frac {21 y}{50} = 0 \]

24097

\[ {} y^{\prime \prime }+5 y^{\prime }-6 y = x^{3} \]

24098

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

24099

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

24100

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

24101

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

24102

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

24103

\[ {} y^{\prime \prime }-9 y = {\mathrm e}^{x}+3 \,{\mathrm e}^{-3 x} \]

24104

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

24105

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

24109

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

24111

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

24120

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

24121

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

24122

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

24123

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

24125

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

24126

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

24127

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

24128

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

24129

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

24132

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

24135

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

24137

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

24138

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

24141

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

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

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

24149

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

24151

\[ {} 6 x^{2} y^{\prime \prime }-5 x y^{\prime }+4 y = 0 \]

24152

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

24153

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

24154

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

24155

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

24156

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

24157

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 \]

24158

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

24159

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

24160

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

24161

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

24162

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

24169

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

24170

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

24171

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

24174

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

24176

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

24177

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

24178

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

24179

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

24183

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

24184

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

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

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

24191

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

24193

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

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

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

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

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

24552

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

24553

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

24555

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

24556

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

24575

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

24576

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

24581

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

24584

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

24585

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

24586

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

24587

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

24588

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

24589

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

24590

\[ {} y^{\prime \prime }-4 y^{\prime }+7 y = 0 \]

24592

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

24593

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

24602

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

24604

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

24617

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

24628

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

24635

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

24636

\[ {} y^{\prime \prime }+4 y = 8 \]

24638

\[ {} y^{\prime \prime }+4 y^{\prime }-5 y = 20 \]

24651

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

24652

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

24653

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 27 x^{2} \]

24654

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = -6 x^{2}-8 x +4 \]

24655

\[ {} y^{\prime \prime }+4 y = 15 \,{\mathrm e}^{x}-8 x \]

24656

\[ {} y^{\prime \prime }+4 y = 15 \,{\mathrm e}^{x}-8 x^{2} \]

24657

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

24658

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

24659

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

24660

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