5.3.12 Problems 1101 to 1200

Table 5.57: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

6044

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

6045

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

6058

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

6062

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

6066

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

6067

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

6068

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

6087

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

6088

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

6094

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

6103

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

6110

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

6122

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

6124

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

6183

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

6184

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

6185

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

6186

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

6188

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

6190

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

6191

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

6202

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

6203

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

6204

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

6205

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

6206

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

6207

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

6212

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

6231

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

6235

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

6236

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

6240

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

6251

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

6253

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

6255

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

6258

\[ {} s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2} \]

6261

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

6274

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

6276

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

6281

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

6295

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

6298

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

6309

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

6325

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

6328

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

6332

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

6336

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

6338

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

6341

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

6344

\[ {} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]

6346

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

6351

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

6381

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

6382

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

6383

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

6384

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

6385

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

6386

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

6407

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

6408

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

6413

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

6414

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

6417

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

6436

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

6439

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

6457

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

6461

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

6490

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

6491

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

6528

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

6560

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

6571

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

6574

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

6585

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

6586

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

6610

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

6611

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

6613

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

6614

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

6629

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

6630

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

6636

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

6647

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

6652

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

6658

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

6661

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

6670

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

6671

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

6673

\[ {} 16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]

6674

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

6675

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

6676

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

6677

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

6682

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

6685

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

6687

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

6689

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

6690

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

6699

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

6700

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