5.17.5 Problems 401 to 500

Table 5.885: Second order, non-linear and homogeneous

#

ODE

Mathematica

Maple

15236

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

15238

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

15239

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

15240

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

15242

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

15251

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

15252

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

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

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

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

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

16908

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

16913

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

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

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

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

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

16940

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

16941

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

16942

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

16943

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

16944

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

16948

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

16949

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

16950

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

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

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

17546

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

17549

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

17566

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

17971

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

17976

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

17977

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

17978

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

17979

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

17982

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

17985

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

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

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

17991

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

17992

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

18044

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

18187

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

18188

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

18190

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

18192

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

18194

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

18195

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

18196

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

18199

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

18205

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

18209

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

18233

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

18239

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

18244

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

18247

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

18270

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

18487

\[ {}x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]

18531

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

18536

\[ {}v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

18538

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

18567

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

18568

\[ {}\phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

18596

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

18597

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

18609

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

18610

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

18611

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

18613

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

18701

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

18702

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

18952

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

18953

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

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

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