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