|
# |
ODE |
Mathematica |
Maple |
|
\[
{}\left (x -y\right ) y^{\prime } = x +y+1
\] |
✓ |
✓ |
|
|
\[
{}x -y-2-\left (2 x -2 y-3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}x \cos \left (x \right ) y^{\prime }+\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y = 1
\] |
✓ |
✓ |
|
|
\[
{}y-\sin \left (x^{2}\right ) x +x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } x \ln \left (x \right )+y = 2 \ln \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y+\sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\left (1+x +x y^{2}\right ) y^{\prime }+y+y^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2}+\left (x -\frac {1}{y}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{5} {\mathrm e}^{x^{3}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {\tan \left (y\right )}{1+x} = \left (1+x \right ) {\mathrm e}^{x} \sec \left (y\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {\tan \left (y\right )}{x} = \frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}}
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime }+\frac {y \ln \left (y\right )}{x} = \frac {y}{x^{2}}-\ln \left (y\right )^{2}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime }+x = x \,{\mathrm e}^{\left (n -1\right ) y}
\] |
✓ |
✓ |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime }-y \sec \left (x \right ) = y^{3} \tan \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
✓ |
✓ |
|
|
\[
{}x +y y^{\prime } = \frac {a^{2} \left (x y^{\prime }-y\right )}{x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}1+4 x y+2 y^{2}+\left (1+4 x y+2 x^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (y^{4} x^{4}+x^{2} y^{2}+x y\right ) y+\left (y^{4} x^{4}-x^{2} y^{2}+x y\right ) x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y \left (x y+2 x^{2} y^{2}\right )+x \left (x y-x^{2} y^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (20 x^{2}+8 x y+4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+x y+y^{2}+y^{3}\right ) x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {\left (x +y-a \right ) y^{\prime }}{x +y-b} = \frac {x +y+a}{x +y+b}
\] |
✓ |
✓ |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
✓ |
✓ |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \left (4 x +y+1\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = x \sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+y \ln \left (y\right ) = x y \,{\mathrm e}^{x}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x \left (-a^{2}+x^{2}+y^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+x^{2}+y^{2}}{2 x y}
\] |
✓ |
✓ |
|
|
\[
{}x +y y^{\prime } = m \left (x y^{\prime }-y\right )
\] |
✓ |
✓ |
|
|
\[
{}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y \left (2 x^{2} y+{\mathrm e}^{x}\right )-\left ({\mathrm e}^{x}+y^{3}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime }+b y^{2} = a \cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y}
\] |
✓ |
✓ |
|
|
\[
{}x^{2}+y^{2}+x -\left (2 x^{2}+2 y^{2}-y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}y \left (1+\frac {1}{x}\right )+\cos \left (y\right )+\left (x +\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (2 x +2 y+3\right ) y^{\prime } = x +y+1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (2 \ln \left (x \right )+1\right )}{\sin \left (y\right )+y \cos \left (y\right )}
\] |
✓ |
✓ |
|
|
\[
{}s^{\prime }+x^{2} = x^{2} {\mathrm e}^{3 s}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x +y\right )+\cos \left (x +y\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {\tan \left (y\right )}{x} = \frac {\tan \left (y\right ) \sin \left (y\right )}{x^{2}}
\] |
✓ |
✗ |
|
|
\[
{}x^{2}-a y = \left (a x -y^{2}\right ) y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y-x y^{\prime }+x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }+2 x \tan \left (y\right ) = x^{3}
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0
\] |
✓ |
✓ |
|
|
\[
{}y = \sin \left (x \right ) y^{\prime }+\cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = x +y y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}\left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = \left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{2}-3 x y y^{\prime } = 2 y^{2}+x^{3}
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = a \left (y^{2}+y^{\prime }\right )
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = b \left (1+x^{2} y^{\prime }\right )
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\cot \left (y\right )-\tan \left (x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-x \,a^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x +2 y^{3}\right ) y^{\prime } = y
\] |
✓ |
✓ |
|
|
\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}1+y^{2}-x y y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {6 x -2 y-7}{2 x +3 y-6}
\] |
✓ |
✓ |
|
|
\[
{}2 x +y+1+\left (4 x +2 y-1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y \sin \left (x \right ) = 1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}\left (x +2 y^{3}\right ) y^{\prime } = y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+p \left (x \right ) y = q \left (x \right ) y^{n}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+x \sin \left (2 y\right ) = x^{3} \cos \left (y\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}a^{2}-2 x y-y^{2}-\left (x +y\right )^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y-\left (y^{3}+x^{3}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x y \sin \left (x y\right )+\cos \left (x y\right )\right ) y+\left (x y \sin \left (x y\right )-\cos \left (x y\right )\right ) y^{\prime } = 0
\] |
✗ |
✗ |
|
|
\[
{}y+\frac {y^{3}}{3}+\frac {x^{2}}{2}+\frac {\left (x y^{2}+x \right ) y^{\prime }}{4} = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x^{2} y^{4}+2 x y+\left (2 y^{2} x^{3}-x^{2}\right ) y^{\prime } = 0
\] |
✗ |
✗ |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x y \left (-x y^{\prime }+y\right ) = x +y y^{\prime }
\] |
✓ |
✓ |
|