5.6.6 Problems 501 to 600

Table 5.557: Second order non-linear ODE

#

ODE

Mathematica

Maple

14305

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

14306

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

14307

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

14308

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

14489

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

14986

\[ {}y^{2} y^{\prime \prime } = 8 x^{2} \]

15215

\[ {}y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \]

15216

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

15217

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

15218

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

15219

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

15220

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

15222

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

15228

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

15229

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

15230

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

15232

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

15233

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

15234

\[ {}y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \]

15235

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

15236

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

15238

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

15239

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

15240

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

15242

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

15250

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

15251

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

15252

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

15253

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

15254

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

15255

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

15256

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

15257

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

15258

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

15259

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

15260

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

15261

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

15265

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

15268

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

15550

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

15576

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

15786

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

15787

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

16248

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

16249

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

16405

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

16622

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

16908

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

16913

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

16914

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

16926

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

16929

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

16930

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

16931

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

16932

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

16933

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

16934

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

16936

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

16937

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

16939

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

16940

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

16941

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

16942

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

16943

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

16944

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

16945

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

16946

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

16947

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

16948

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

16949

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

16950

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

17173

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

17174

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

17175

\[ {}x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0 \]

17176

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

17177

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

17178

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

17179

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

17184

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

17546

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

17549

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

17564

\[ {}y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi } \]

17566

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

17685

\[ {}y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right ) \]

17686

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right ) \]

17971

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

17974

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

17976

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

17977

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

17978

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

17979

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

17980

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

17981

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

17982

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

17983

\[ {}x \left (x^{2} y^{\prime }+2 x y\right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 x y y^{\prime }+4 y^{2}-1 = 0 \]

17984

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

17985

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

17986

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

17987

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

17988

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