5.3.60 Problems 5901 to 6000

Table 5.165: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

18093

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

18109

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

18111

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

18114

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

18115

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

18119

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

18122

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

18123

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

18124

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

18127

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

18128

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

18129

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

18130

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

18132

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

18133

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

18134

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

18139

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

18141

\[ {} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0 \]

18144

\[ {} \left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (-2 y+x y^{\prime }\right ) = 0 \]

18146

\[ {} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x \]

18148

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

18151

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

18153

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

18158

\[ {} 5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \]

18159

\[ {} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0 \]

18162

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

18165

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

18181

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

18185

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

18187

\[ {} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

18190

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

18192

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

18200

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

18201

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

18216

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

18218

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

18221

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

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

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

18238

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

18350

\[ {} 2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right ) \]

18356

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

18403

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \]

18409

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

18413

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

18420

\[ {} \left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y = 6 \ln \left (1+x \right ) \]

18421

\[ {} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x \]

18422

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

18423

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

18424

\[ {} \left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 y^{\prime } \left (1+x \right )+6 y = 6 \]

18425

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

18426

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

18427

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

18428

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

18430

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

18431

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

18432

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

18433

\[ {} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x} = x \,{\mathrm e}^{2 x}-1 \]

18434

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

18436

\[ {} y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1} \]

18438

\[ {} y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \]

18439

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

18446

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

18447

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

18449

\[ {} 4 x y^{\prime \prime }+2 y^{\prime }+y = 1 \]

18450

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

18452

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

18453

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

18454

\[ {} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x} \]

18455

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

18456

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

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

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

18470

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

18471

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

18490

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

18492

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

18495

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

18516

\[ {} \left [x_{1}^{\prime }\left (t \right ) = -2 t x_{1} \left (t \right )^{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )+t}{t}\right ] \]

18517

\[ {} [x_{1}^{\prime }\left (t \right ) = {\mathrm e}^{t -x_{1} \left (t \right )}, x_{2}^{\prime }\left (t \right ) = 2 \,{\mathrm e}^{x_{1} \left (t \right )}] \]

18521

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

18522

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

18523

\[ {} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )}\right ] \]

18534

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