4.4.36 Problems 3501 to 3600

Table 4.615: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

14724

\[ {} 9 y^{\prime \prime }+6 y^{\prime }+5 y = 0 \]

14725

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+37 y = 0 \]

14812

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

14813

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

14814

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

14815

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

14816

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

14817

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

14818

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

14819

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

14820

\[ {} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

14821

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

14831

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

14832

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

14833

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

14839

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

14840

\[ {} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0 \]

14927

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

14928

\[ {} y^{\prime \prime }+y^{\prime }-12 y = 0 \]

14930

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

14943

\[ {} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0 \]

14945

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

14947

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

14948

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

14949

\[ {} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0 \]

14950

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

14951

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

14952

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

14953

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

14954

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

14955

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

14956

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

14957

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

14958

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

14959

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

14960

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

14961

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

14962

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

14963

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

14964

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

14965

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

14966

\[ {} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0 \]

14979

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

14980

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

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

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

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

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

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

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

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

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

15187

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

15196

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

15198

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

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

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

15208

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

15209

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

15213

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

15217

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

15221

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

15223

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

15224

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

15239

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

15258

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

15261

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

15263

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

15266

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

15267

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

15271

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

15272

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