4.24.54 Problems 5301 to 5400

Table 4.1459: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

23547

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

23577

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

23581

\[ {} x^{2} y^{\prime \prime }+4 x y^{\prime }-10 y = x \ln \left (x \right ) \]

23582

\[ {} 3 x^{2} y^{\prime \prime }-2 x y^{\prime }-8 y = 5+3 x \]

23584

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

23585

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

23588

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

23590

\[ {} 3 x y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = 3 \cos \left (x \right ) \]

23618

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

23619

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

23654

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

23655

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

23656

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

23657

\[ {} 2 x^{2} y^{\prime \prime }+7 x y^{\prime }-3 y = \frac {\ln \left (x \right )}{x^{2}} \]

23658

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \]

23666

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

23667

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

23668

\[ {} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x} = 0 \]

23669

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

23877

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

23962

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

23963

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

24036

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

24037

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

24038

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

24039

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

24040

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

24041

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

24042

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

24043

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

24070

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

24080

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

24082

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

24083

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

24125

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

24126

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

24127

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

24128

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

24151

\[ {} 6 x^{2} y^{\prime \prime }-5 x y^{\prime }+4 y = 0 \]

24152

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

24153

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

24154

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

24155

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

24156

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

24157

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 \]

24158

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

24159

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

24160

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

24177

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

24193

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

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

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

24992

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

24993

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

24994

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

24995

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

24997

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

24998

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

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

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

25005

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

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

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

25010

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

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

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

25019

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

25020

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

25021

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

25022

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

25023

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

25024

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

25203

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

25206

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

25261

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

25262

\[ {} y^{\left (5\right )}+t y^{\prime \prime }-3 y = 0 \]

25296

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

25299

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

25300

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

25301

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

25302

\[ {} y^{\prime \prime }+\sqrt {t}\, y^{\prime }+y = \sqrt {t} \]

25303

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

25304

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