4.6.9 Problems 801 to 900

Table 4.741: Second order non-linear ODE

#

ODE

Mathematica

Maple

Sympy

16545

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

16546

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

16547

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

16548

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

16552

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

16555

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

16837

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

16863

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

17073

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

17074

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

17535

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

17536

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

17692

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

17909

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

18195

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

18200

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

18201

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

18213

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

18216

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

18217

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

18218

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

18219

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

18220

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

18221

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

18223

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

18224

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

18226

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

18227

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

18228

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

18229

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

18230

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

18231

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

18232

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

18233

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

18234

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

18235

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

18236

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

18237

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

18460

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

18461

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

18462

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

18463

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

18464

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

18465

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

18466

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

18471

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

18833

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

18836

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

18851

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

18853

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

18971

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

18972

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

19257

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

19260

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

19262

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

19263

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

19264

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

19265

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

19266

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

19267

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

19268

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

19269

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

19270

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

19271

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

19272

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

19273

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

19274

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

19277

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

19278

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

19329

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

19330

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

19473

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

19474

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

19476

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

19477

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

19478

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

19480

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

19481

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

19482

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

19483

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

19484

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

19485

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

19491

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

19495

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

19508

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

19519

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

19525

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

19530

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

19533

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

19556

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

19773

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

19817

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

19822

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

19824

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

19853

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

19854

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

19882

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

19883

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

19886

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

19895

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