5.3.19 Problems 1801 to 1900

Table 5.83: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

6942

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

6943

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

6946

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

6951

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

6955

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

6956

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

6958

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

6959

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

6961

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

6962

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

6963

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

6965

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

6967

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

6968

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

6971

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

6973

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

6998

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

7010

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

7012

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

7019

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

7023

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

7030

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

7033

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

7036

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

7045

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

7047

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

7048

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

7130

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

7132

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

7135

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

7139

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

7141

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

7142

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

7145

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

7146

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

7147

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

7148

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

7151

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

7152

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

7153

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

7154

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

7156

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

7157

\[ {} y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {f \left (x \right ) a +b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0 \]

7158

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

7159

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

7165

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

7170

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

7175

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

7177

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

7178

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

7179

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

7180

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

7193

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

7197

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

7201

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

7202

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

7203

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

7222

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

7223

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

7229

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

7238

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

7245

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

7257

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

7259

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

7318

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

7319

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

7320

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

7321

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

7323

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

7325

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

7326

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

7337

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

7338

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

7339

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

7340

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

7341

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

7342

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

7347

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

7366

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

7370

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

7371

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

7375

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

7386

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

7388

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

7390

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

7393

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

7396

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

7409

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

7411

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

7416

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

7430

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

7433

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

7444

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

7460

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

7463

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

7467

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

7471

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

7473

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

7474

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

7475

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