|
# |
ODE |
Mathematica |
Maple |
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right ) = x \cos \left (\frac {y}{x}\right )
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = \sqrt {9 x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}2 x y y^{\prime }-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}-2 y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}2 x \left (y+2 x \right ) y^{\prime } = \left (4 x -y\right ) y
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = -y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{2 x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {1-y^{2}}{2 x y+2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (1-y \,{\mathrm e}^{x y}\right ) {\mathrm e}^{-x y}}{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{x^{{2}/{3}}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \ln \left (x \right ) x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+1}
\] |
✓ |
✓ |
|
|
\[
{}{\mathrm e}^{x +y} y^{\prime }-1 = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
✓ |
✓ |
|
|
\[
{}y-\left (x -1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x \left (y-1\right )}{x^{2}+3}
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = 3-2 x^{2} y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \left (y^{2}-1\right )}{2 \left (x -1\right ) \left (x -2\right )}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+2
\] |
✓ |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = a x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 \sqrt {y-1}}{3}
\] |
✓ |
✓ |
|
|
\[
{}m v^{\prime } = m g -k v^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = 4 \,{\mathrm e}^{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 2 x^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 x y}{-x^{2}+1} = 4 x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {4}{\left (x^{2}+1\right )^{2}}
\] |
✓ |
✓ |
|
|
\[
{}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 8 \sin \left (x \right )^{3}
\] |
✓ |
✓ |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right )
\] |
✓ |
✓ |
|
|
\[
{}1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 2 \ln \left (x \right ) x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\alpha y = {\mathrm e}^{\beta x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {m y}{x} = \ln \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 4 x
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+\frac {2 x}{-t +4} = 5
\] |
✓ |
✓ |
|
|
\[
{}y-{\mathrm e}^{x}+y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = \ln \left (x \right ) x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right ) = x \cos \left (\frac {y}{x}\right )
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = \sqrt {9 x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}2 x y y^{\prime }-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}-2 y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}2 x \left (y+2 x \right ) y^{\prime } = \left (4 x -y\right ) y
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {-2 x +4 y}{x +y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-\sqrt {x^{2}+y^{2}}}{x}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = \sqrt {4 x^{2}-y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {a y+x}{a x -y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {\tan \left (x \right ) y}{2} = 2 y^{3} \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{2 x} = 6 y^{{1}/{3}} x^{2} \ln \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
✓ |
✓ |
|
|
\[
{}2 x \left (y^{\prime }+x^{2} y^{3}\right )+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right ) = 2 \left (b -a \right ) y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {6 y}{x} = \frac {3 y^{{2}/{3}} \cos \left (x \right )}{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+4 x y = 4 x^{3} \sqrt {y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{2 x \ln \left (x \right )} = 2 x y^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi }
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime }+y \cot \left (x \right ) = \frac {8 \cos \left (x \right )^{3}}{y}
\] |
✓ |
✓ |
|
|
\[
{}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = x y^{2}
\] |
✓ |
✓ |
|