|
# |
ODE |
Mathematica |
Maple |
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
✗ |
✗ |
|
|
\[
{}x \left (1+y\right )^{2} = \left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y \,{\mathrm e}^{x^{2}} = \sinh \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = 1
\] |
✓ |
✓ |
|
|
\[
{}5 y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = 4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right )
\] |
✓ |
✓ |
|
|
\[
{}10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}1+y-\left (1-x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y-a +x^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
✓ |
✓ |
|
|
\[
{}1+s^{2}-\sqrt {t}\, s^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y+x +x y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x +y+\left (y-x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}2 \sqrt {s t}-s+t s^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}t -s+t s^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{2} y^{\prime } x = y^{3}+x^{3}
\] |
✓ |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )
\] |
✓ |
✓ |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x +2 y+1-\left (4 y+2 x +3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {-x y^{\prime }+y}{\sqrt {x^{2}+y^{2}}} = m
\] |
✓ |
✓ |
|
|
\[
{}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {a y}{x} = \frac {1+x}{x}
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1
\] |
✓ |
✓ |
|
|
\[
{}s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {n y}{x} = {\mathrm e}^{x} x^{n}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1 = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
✓ |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}3 y^{\prime } y^{2}-a y^{3}-x -1 = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } \left (x^{2} y^{3}+x y\right ) = 1
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = \left (y \ln \left (x \right )-2\right ) y
\] |
✓ |
✓ |
|
|
\[
{}y-y^{\prime } \cos \left (x \right ) = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right )
\] |
✓ |
✓ |
|
|
\[
{}x^{2}+y+\left (x -2 y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y-3 x^{2}-\left (4 y-x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (y^{3}-x \right ) y^{\prime } = y
\] |
✓ |
✓ |
|
|
\[
{}\frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (y+2 x \right ) y^{\prime }}{\left (x +y\right )^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}}
\] |
✓ |
✓ |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}x +y y^{\prime } = \frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y = x y^{\prime }+y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}-\sqrt {3}
\] |
✓ |
✓ |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0
\] |
✓ |
✓ |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+\frac {1}{2 y} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 \sqrt {{| y|}} = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y^{2} = 1
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-\sin \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+3 y = 0
\] |
✓ |
✓ |
|
|
\[
{}2 x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = x^{2}+2 x -1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
✓ |
✓ |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }-\left (\ln \left (x \right )+1\right ) y = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 1-x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x -1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 1-y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 1+y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 4-y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = -x y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = y^{2}-x^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x +y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
✓ |
✓ |
|