5.3.54 Problems 5301 to 5400

Table 5.141: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

18132

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

18134

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

18137

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

18144

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

18149

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

18151

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

18159

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

18163

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

18167

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

18168

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

18172

\[ {} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime } = 0 \]

18176

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

18187

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

18200

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

18205

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

18207

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

18209

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

18210

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

18211

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

18212

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

18213

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

18214

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

18215

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

18216

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

18250

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

18251

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

18273

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \]

18281

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

18282

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

18283

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

18284

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

18338

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

18339

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

18343

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

18349

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

18350

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

18351

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

18356

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

18357

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

18358

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

18365

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

18366

\[ {} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}} = 0 \]

18387

\[ {} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y = 0 \]

18388

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

18389

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

18416

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

18423

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

18425

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

18427

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

18434

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

18460

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

18463

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

18465

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

18467

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

18469

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

18476

\[ {} 2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g \]

18478

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

18479

\[ {} \frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0 \]

18480

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

18488

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

18491

\[ {} \sqrt {t^{2}+T} = T^{\prime } \]

18496

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

18497

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

18508

\[ {} 4 {y^{\prime }}^{3} y-2 x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }+x^{3} = 16 y^{2} \]

18526

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

18529

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

18530

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

18532

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

18538

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

18539

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

18540

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

18541

\[ {} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0 \]

18542

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

18543

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

18547

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

18563

\[ {} \sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime } = 0 \]

18565

\[ {} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime } = 0 \]

18566

\[ {} x^{3}+4 x y+y^{2}+\left (2 x^{2}+2 x y+4 y^{3}\right ) y^{\prime } = 0 \]

18569

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

18572

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

18577

\[ {} \left (6 x -5 y+4\right ) y^{\prime } = 1+2 x -y \]

18578

\[ {} \left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2 \]

18620

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

18621

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

18622

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

18623

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

18624

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

18625

\[ {} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3} \]

18631

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

18632

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

18663

\[ {} \left (3 x +4 y\right ) y^{\prime }+y-2 x = 0 \]

18665

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

18666

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

18667

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

18669

\[ {} 2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0 \]

18670

\[ {} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y} = 0 \]

18680

\[ {} 3 x^{2} y^{4}+2 x y+\left (2 y^{3} x^{3}-x^{2}\right ) y^{\prime } = 0 \]

18683

\[ {} 2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0 \]

18684

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

18687

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