4.3.56 Problems 5501 to 5600

Table 4.395: Second order ode

#

ODE

Mathematica

Maple

Sympy

17054

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

17055

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

17056

\[ {} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

17057

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

17058

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

17059

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

17060

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

17061

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

17062

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

17063

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4} \]

17064

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

17065

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

17066

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

17067

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

17068

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

17069

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

17070

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

17071

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

17072

\[ {} y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \]

17073

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

17074

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

17075

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

17076

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

17078

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

17079

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

17080

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

17081

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

17082

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

17083

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

17084

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

17085

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

17086

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

17087

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

17088

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

17089

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

17090

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

17091

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

17092

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

17093

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

17094

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

17095

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

17096

\[ {} x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0 \]

17097

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

17098

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

17099

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

17100

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

17101

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

17102

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

17103

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

17104

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

17105

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

17106

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

17107

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

17108

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

17109

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

17110

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

17111

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

17112

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

17113

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

17116

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

17137

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y = 0 \]

17138

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

17139

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

17140

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

17141

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

17142

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

17143

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

17144

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

17145

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

17146

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

17147

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

17148

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

17149

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

17209

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

17210

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

17211

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

17212

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

17213

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

17214

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

17215

\[ {} x^{\prime \prime }+x = t \]

17216

\[ {} x^{\prime \prime }+6 x^{\prime } = 12 t +2 \]

17217

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

17218

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

17219

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

17220

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

17466

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

17467

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

17468

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

17469

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

17470

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

17471

\[ {} y^{\prime \prime }-t y = \frac {1}{\pi } \]

17472

\[ {} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d \]

17473

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

17474

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

17475

\[ {} y^{\prime \prime }+y^{\prime }+16 y = 0 \]

17476

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

17477

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

17478

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

17479

\[ {} \left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right ) \]

17480

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