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