4.17.9 Problems 801 to 850

Table 4.1171: Second order, non-linear and homogeneous

#

ODE

Mathematica

Maple

Sympy

23161

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

23162

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

23163

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

23165

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

23222

\[ {} y^{\prime \prime }-\tan \left (x \right ) y^{\prime }-\frac {\tan \left (x \right ) y}{x} = \frac {y^{3}}{x^{3}} \]

23233

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

23344

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

23350

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

23351

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

23352

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

23353

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

23358

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

24040

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

24043

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

24070

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

24082

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

24985

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

24986

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

24987

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

24988

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

24989

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

24990

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

24991

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

24994

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

24995

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

24997

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

24999

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

25000

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

25001

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

25002

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

25003

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

25004

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

25006

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

25007

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

25008

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

25009

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

25011

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

25012

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

25013

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

25014

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

25015

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

25016

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

25017

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

25018

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

25021

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

25022

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

25206

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

25296

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

25299

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

25304

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