|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x -y+\left (2 y-x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \frac {\sin \left (y\right )}{y}-2 \,{\mathrm e}^{-x} \sin \left (x \right )+\frac {\left (\cos \left (y\right )+2 \,{\mathrm e}^{-x} \cos \left (x \right )\right ) y^{\prime }}{y} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 3 x^{2} y+2 x y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = {\mathrm e}^{2 x}+y-1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \frac {y^{\prime }}{\frac {x}{y}-\sin \left (y\right )} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y+\left (2 x y-{\mathrm e}^{-2 y}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y y^{\prime } = 1+x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (y^{4}+1\right ) y^{\prime } = x^{4}+1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \left (x -1\right ) y^{\prime } = y \left (y+1\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \sqrt {x^{2}-y^{2}}+y = x y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y y^{\prime } = \left (x +y\right )^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {4 y-7 x}{5 x -y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x y^{\prime }-4 \sqrt {y^{2}-x^{2}} = y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y y^{\prime } = x^{2}+y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {x +y}{x -y}
\]
|
✓ |
✗ |
✓ |
|
|
\[
{} t y^{\prime }+y = t^{2} y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y \left (t y^{3}-1\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+\frac {3 y}{t} = t^{2} y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} t^{2} y^{\prime }+2 t y-y^{3} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 3 t y^{\prime }+9 y = 2 t y^{{5}/{3}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y+\sqrt {y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = r y-k^{2} y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = a y+b y^{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+3 t y = 4-4 t^{2}+y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (3 x-y \right ) x^{\prime }+9 y -2 x = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 1 = \left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime }+\left (1+x \right ) y = x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \frac {\sqrt {x}\, y^{\prime }}{y} = 1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x y y^{\prime }+\ln \left (x \right ) = -y^{2}-1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (2-x \right ) y^{\prime } = y+2 \left (2-x \right )^{5}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime } = -\frac {1}{\ln \left (x \right )}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 4 x y y^{\prime } = 8 x^{2}+5 y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+y-y^{{1}/{4}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} x^{\prime } = \frac {x \sqrt {6 x-9}}{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = -x^{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x \sqrt {1+y^{2}}+y y^{\prime } \sqrt {x^{2}+1} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \sqrt {-x^{2}+1}\, y^{\prime }+\sqrt {1-y^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {2 x y}{x^{2}+y^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x +y\right ) y^{\prime } = y-x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 3 y-7 x +7 = \left (3 x -7 y-3\right ) y^{\prime }
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x +2 y+1\right ) y^{\prime } = 2 x +4 y+3
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \left (x +y\right )^{2} y^{\prime } = a^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime }-4 y = x^{2} \sqrt {y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \cos \left (x \right ) y^{\prime } = y \sin \left (x \right )+\cos \left (x \right )^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 x y-x^{3}+x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime }+y = x y^{2} \ln \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } \left (x^{2} y^{3}+x y\right ) = 1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x -y^{2}+2 x y y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {y^{2}}{3}+\frac {2}{3 x^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x y^{\prime }-3 y+y^{2} = 4 x^{2}-4 x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y^{2}+\frac {1}{x^{4}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime } = \left (1+y^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } \left (x^{2}+y^{2}+3\right ) = 2 x \left (2 y-\frac {x^{2}}{y}\right )
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {x -y^{2}}{2 y \left (x +y^{2}\right )}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x \left (x +y\right )+a^{2}\right ) y^{\prime } = y \left (x +y\right )+b^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = k y+f \left (x \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y^{2}-x^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {x +y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y-x y^{\prime }}{x^{2}+y^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {\sin \left (\frac {x}{y}\right )}{y}-\frac {y \cos \left (\frac {y}{x}\right )}{x^{2}}+1+\left (\frac {\cos \left (\frac {y}{x}\right )}{x}-\frac {x \sin \left (\frac {x}{y}\right )}{y^{2}}+\frac {1}{y^{2}}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} \frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left (x^{2} y^{2}-1\right ) y^{\prime }+2 x y^{3} = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = 2 x y-x^{3}+x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} 2 x^{3}+3 x^{2} y+y^{2}-y^{3}+\left (2 y^{3}+3 x y^{2}+x^{2}-x^{3}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \sqrt {y-x}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \sqrt {y-x}+1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \sqrt {y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y \ln \left (y\right )
\]
|
✓ |
✓ |
✓ |
|