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