4.3.53 Problems 5201 to 5300

Table 4.469: Second order ode

#

ODE

Mathematica

Maple

Sympy

14981

\[ {} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0 \]

14982

\[ {} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0 \]

14983

\[ {} x^{\prime \prime }+\left (1+x^{2}\right ) x^{\prime }+x^{3} = 0 \]

15031

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

15032

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

15033

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

15034

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

15035

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

15036

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

15037

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

15038

\[ {} 2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \]

15039

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

15040

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = 0 \]

15041

\[ {} 4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]

15042

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

15043

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

15044

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

15045

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

15046

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

15047

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

15048

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

15049

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

15050

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

15051

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

15052

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

15053

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

15054

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

15055

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

15056

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

15057

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

15058

\[ {} x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

15059

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

15060

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

15065

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

15066

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

15067

\[ {} \left (\cos \left (t \right ) t -\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0 \]

15068

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

15069

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

15070

\[ {} \tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0 \]

15071

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

15072

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

15073

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

15074

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

15075

\[ {} x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \]

15076

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

15077

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

15078

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

15079

\[ {} t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \]

15080

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

15081

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

15082

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

15083

\[ {} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]

15084

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

15085

\[ {} 3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \]

15086

\[ {} t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \]

15087

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

15181

\[ {} y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]

15182

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

15184

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

15185

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

15186

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

15187

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

15188

\[ {} x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \]

15189

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

15190

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

15196

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

15197

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

15198

\[ {} y^{\prime \prime } = 3 \sqrt {y} \]

15199

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

15200

\[ {} u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \]

15201

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

15202

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

15203

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

15204

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

15206

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

15207

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

15208

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

15209

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

15212

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

15213

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

15215

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

15216

\[ {} x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

15217

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

15221

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

15222

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

15223

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

15224

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

15239

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

15241

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

15251

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

15253

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

15254

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

15258

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

15259

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

15261

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

15263

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

15265

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

15266

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

15267

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

15268

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