|
# |
ODE |
Mathematica |
Maple |
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{3} \sin \left (x \right )^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \left (9 x -y\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \left (4 x +y+2\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (3 x -3 y+1\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (\ln \left (x y\right )-1\right )}{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 2 x \left (x +y\right )^{2}-1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +2 y-1}{2 x -y+3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right ) = q \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x}
\] |
✓ |
✓ |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {1+x}} = \frac {1}{2 \sqrt {1+x}}
\] |
✓ |
✓ |
|
|
\[
{}y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
✗ |
✗ |
|
|
\[
{}\cos \left (x y\right )-x y \sin \left (x y\right )-x^{2} \sin \left (x y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y+3 x^{2}+x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2}-2 x +2 x y y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}4 \,{\mathrm e}^{2 x}+2 x y-y^{2}+\left (x -y\right )^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}y \cos \left (x y\right )-\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = 8 \,{\mathrm e}^{3 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+3 y = 2 \,{\mathrm e}^{-t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+2 y = 4 t
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 6 \cos \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 5 \sin \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+2 y = 2 \operatorname {Heaviside}\left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+2 y = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = \delta \left (t -5\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = \delta \left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+4 y = 3 \delta \left (t -1\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right )
\] |
✓ |
✓ |
|
|
\[
{}5 x y+4 y^{2}+1+\left (x^{2}+2 x y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2} \left (x^{2}+1\right )+y+\left (2 x y+1\right ) y^{\prime } = 0
\] |
✗ |
✗ |
|
|
\[
{}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime } = x \left (y-1\right )+\left (y-1\right )^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 1-x^{5}+\sqrt {x}
\] |
✓ |
✓ |
|
|
\[
{}3 y-2 x +\left (3 x -2\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2}+x -1+\left (2 x y+y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}{\mathrm e}^{2 y}+\left (1+x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (1+x \right ) y^{\prime }-x^{2} y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-2 x}{x}
\] |
✓ |
✓ |
|
|
\[
{}x^{3}+y^{3}-y^{2} y^{\prime } x = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = x^{2}+2
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -2 y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = x +y
\] |
✓ |
✓ |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x +\frac {1}{x}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+2 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\] |
✓ |
✓ |
|
|
\[
{}2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}x y y^{\prime } = \left (1+x \right ) \left (1+y\right )
\] |
✗ |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{y+2 x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{3 y-x +5}
\] |
✓ |
✓ |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x +\left (2-x +2 y\right ) y^{\prime } = x y \left (y^{\prime }-1\right )
\] |
✓ |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 1
\] |
✓ |
✓ |
|
|
\[
{}\left (y^{2}+x \right ) y^{\prime }+y-x^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = x^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \tan \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) y = \cot \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = x^{-x}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+y = x
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = x^{3}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+n y = x^{n}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-n y = x^{n}
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{3}+x \right ) y^{\prime }+y = x
\] |
✓ |
✓ |
|
|
\[
{}\cot \left (x \right ) y^{\prime }+y = x
\] |
✓ |
✓ |
|
|
\[
{}\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime }+y = \cot \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y-\cos \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
✓ |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = \sin \left (2 x \right )
\] |
✓ |
✓ |
|