|
# |
ODE |
Mathematica |
Maple |
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )+2 \cos \left (x \right )\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
✗ |
✗ |
|
|
\[
{}y \,{\mathrm e}^{x y} \cos \left (2 x \right )-2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+2 x +\left (x \,{\mathrm e}^{x y} \cos \left (2 x \right )-3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {\sin \left (y\right )}{y}-2 \sin \left (x \right ) {\mathrm e}^{-x}+\frac {\left (\cos \left (y\right )+2 \,{\mathrm e}^{-x} \cos \left (x \right )\right ) y^{\prime }}{y} = 0
\] |
✓ |
✓ |
|
|
\[
{}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x^{2} y+2 x y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+y-1
\] |
✓ |
✓ |
|
|
\[
{}\frac {y^{\prime }}{\frac {x}{y}-\sin \left (y\right )} = 0
\] |
✓ |
✓ |
|
|
\[
{}y+\left (2 x y-{\mathrm e}^{-2 y}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\] |
✗ |
✗ |
|
|
\[
{}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = 1+x
\] |
✓ |
✓ |
|
|
\[
{}\left (y^{4}+1\right ) y^{\prime } = x^{4}+1
\] |
✓ |
✓ |
|
|
\[
{}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\] |
✓ |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime } = y \left (1+y\right )
\] |
✓ |
✓ |
|
|
\[
{}\sqrt {x^{2}-y^{2}}+y = x y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}x y y^{\prime } = \left (x +y\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {4 y-7 x}{5 x -y}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-4 \sqrt {y^{2}-x^{2}} = y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}}
\] |
✓ |
✓ |
|
|
\[
{}\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}}
\] |
✓ |
✓ |
|
|
\[
{}x y y^{\prime } = x^{2}+y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
✓ |
✗ |
|
|
\[
{}t y^{\prime }+y = t^{2} y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = y \left (t y^{3}-1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {3 y}{t} = t^{2} y^{2}
\] |
✓ |
✓ |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right )
\] |
✓ |
✓ |
|
|
\[
{}3 t y^{\prime }+9 y = 2 t y^{{5}/{3}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = y+\sqrt {y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = r y-k^{2} y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = a y+b y^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+3 t y = 4-4 t^{2}+y^{2}
\] |
✓ |
✓ |
|
|
\[
{}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0
\] |
✓ |
✓ |
|
|
\[
{}1 = \left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+\left (1+x \right ) y = x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y}
\] |
✓ |
✓ |
|
|
\[
{}\frac {\sqrt {x}\, y^{\prime }}{y} = 1
\] |
✓ |
✓ |
|
|
\[
{}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x y y^{\prime }+\ln \left (x \right ) = -y^{2}-1
\] |
✓ |
✓ |
|
|
\[
{}\left (2-x \right ) y^{\prime } = y+2 \left (2-x \right )^{5}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = -\frac {1}{\ln \left (x \right )}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y}
\] |
✓ |
✓ |
|
|
\[
{}4 x y y^{\prime } = 8 x^{2}+5 y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y-y^{{1}/{4}} = 0
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+\sin \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-\cos \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 t x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-3]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+t y \left (t \right ), y^{\prime }\left (t \right ) = t x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+\sin \left (t \right ) y \left (t \right )]
\] |
✗ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 \sin \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )+2 t, y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )-3]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+1, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-3]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )-4, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-6]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{4}-\frac {3 y \left (t \right )}{4}+8, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{2}+y \left (t \right )-\frac {23}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-11, y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )-35]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-3, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+1]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )-35, y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-11]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}+\frac {5 y \left (t \right )}{4}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {7 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{4}+\frac {5 y \left (t \right )}{4}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{4}-\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = 2 x \left (t \right )-\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = \frac {9 x \left (t \right )}{5}-y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {5 y \left (t \right )}{4}\right ]
\] |
✓ |
✓ |
|