5.3.54 Problems 5301 to 5400

Table 5.153: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

14148

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

14151

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

14152

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

14155

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

14168

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

14169

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

14172

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

14173

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

14174

\[ {} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0 \]

14175

\[ {} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0 \]

14176

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

14177

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

14178

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

14179

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

14181

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

14183

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

14184

\[ {} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1 = 0 \]

14187

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

14189

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

14191

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

14192

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

14193

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

14197

\[ {} 8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \]

14213

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

14231

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

14232

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

14246

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

14247

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

14248

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

14249

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

14250

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

14251

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

14252

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

14253

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

14254

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

14255

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

14256

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

14257

\[ {} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime } = \frac {1}{x^{2}} \]

14258

\[ {} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 4 x^{3} {\mathrm e}^{-x^{2}} \]

14259

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

14260

\[ {} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \]

14262

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

14263

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

14266

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

14267

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

14268

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

14270

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

14273

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

14274

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

14275

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

14277

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

14278

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

14279

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

14280

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

14282

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

14283

\[ {} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

14284

\[ {} 2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 y y^{\prime } x +6 y^{2} = 0 \]

14285

\[ {} x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0 \]

14286

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

14287

\[ {} x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \]

14289

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

14290

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

14291

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

14292

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

14295

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

14296

\[ {} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime } = 0 \]

14297

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

14298

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

14300

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

14302

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

14304

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

14316

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

14325

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

14345

\[ {} T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \]

14348

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

14358

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

14360

\[ {} x x^{\prime } = 1-t x \]

14361

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

14388

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

14389

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

14453

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

14454

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

14456

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

14464

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

14530

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

14546

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

14547

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

14550

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

14551

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

14555

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

14556

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

14557

\[ {} 6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0 \]

14558

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

14562

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

14563

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

14564

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

14565

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

14567

\[ {} \frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0 \]

14570

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

14582

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