4.6.11 Problems 1001 to 1100

Table 4.745: Second order non-linear ODE

#

ODE

Mathematica

Maple

Sympy

21442

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

21443

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

21444

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

21445

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

21676

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

21681

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

21728

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

21729

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

21850

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

21873

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

21875

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

21876

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

21877

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

21878

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

21879

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

21880

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

21881

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

21903

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

21904

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

21905

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

22067

\[ {} s^{2} t^{\prime \prime }+s t t^{\prime } = s \]

22069

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

22070

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

22074

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

22075

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

22202

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

22204

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

22412

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

22433

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

22441

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

22446

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

22472

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

22600

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

22604

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

22605

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

22606

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

22613

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

22615

\[ {} y^{\prime \prime } = -\frac {4}{y^{3}} \]

22616

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

22681

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

22694

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

22921

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

23161

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

23162

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

23163

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

23164

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

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

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

23354

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

23358

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

23408

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

24038

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

24040

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

24041

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

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

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

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

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