5.3.63 Problems 6201 to 6300

Table 5.409: Second order ode

#

ODE

Mathematica

Maple

18952

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

18953

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

18956

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

18957

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

18958

\[ {}y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]

18959

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

18960

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

18962

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

18963

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

18965

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

18966

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

18967

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

18968

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

18972

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

18973

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

18974

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

18982

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

18983

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

18987

\[ {}{y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} \]

18989

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

18990

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

18991

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

18993

\[ {}y^{\prime \prime } = \frac {a}{x} \]

18994

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

18996

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

18998

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

18999

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

19000

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

19002

\[ {}y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2} \]

19003

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

19004

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

19005

\[ {}\left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

19006

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

19007

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

19008

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

19009

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0 \]

19010

\[ {}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

19011

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = 0 \]

19012

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

19013

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

19014

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

19015

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

19016

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

19017

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

19018

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

19019

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

19020

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

19021

\[ {}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y = 0 \]

19022

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

19023

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

19024

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

19025

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

19026

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

19028

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

19029

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

19030

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

19031

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

19032

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

19033

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

19034

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

19035

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

19045

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x} \]

19046

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

19159

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

19161

\[ {}2 x^{\prime \prime }+5 x^{\prime }-12 x = 0 \]

19162

\[ {}y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

19163

\[ {}9 x^{\prime \prime }+18 x^{\prime }-16 x = 0 \]

19165

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

19173

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

19174

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

19175

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

19176

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

19177

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}} \]

19178

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

19179

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

19180

\[ {}y^{\prime \prime }+9 y = \sin \left (2 x \right )+\cos \left (2 x \right ) \]

19181

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

19182

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

19184

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

19185

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

19191

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

19192

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

19193

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

19196

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x} \]

19197

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

19200

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

19201

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right ) \]

19202

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

19206

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

19209

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0 \]

19315

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

19316

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

19323

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

19325

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

19326

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

19327

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

19328

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

19329

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

19330

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

19331

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