|
# |
ODE |
Mathematica |
Maple |
|
\[
{}x^{\prime }+5 x = t
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+\left (a +\frac {1}{t}\right ) x = b
\] |
✓ |
✓ |
|
|
\[
{}T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right )
\] |
✓ |
✓ |
|
|
\[
{}2 x y-\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}1+y \,{\mathrm e}^{x}+x \,{\mathrm e}^{x} y+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }+\sin \left (y\right )-y \sin \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}{\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}V^{\prime }\left (x \right )+2 y y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b = 0
\] |
✓ |
✓ |
|
|
\[
{}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {x^{2}+t \sqrt {x^{2}+t^{2}}}{t x}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
✓ |
✓ |
|
|
\[
{}\tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+y = x^{3}
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = x^{2} y y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{2 t}
\] |
✓ |
✓ |
|
|
\[
{}y \sin \left (x \right )+y^{\prime } \cos \left (x \right ) = 1
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = x+\sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2} = 9 y^{4}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\] |
✓ |
✓ |
|
|
\[
{}x^{2}+{y^{\prime }}^{2} = 1
\] |
✓ |
✓ |
|
|
\[
{}y = x y^{\prime }+\frac {1}{y}
\] |
✓ |
✓ |
|
|
\[
{}x = {y^{\prime }}^{3}-y^{\prime }+2
\] |
✗ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y}{x +y^{3}}
\] |
✓ |
✓ |
|
|
\[
{}y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\] |
✗ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 4
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 y-x -4}{2 x -y+5}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-\frac {y}{1+x}+y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = y^{2}+x
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x y^{3}+x^{2}
\] |
✗ |
✗ |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
✓ |
✓ |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y = 5 x y^{\prime }-{y^{\prime }}^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2
\] |
✓ |
✓ |
|
|
\[
{}y \left (x -y\right )-x^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }+5 x = 10 t +2
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}}
\] |
✓ |
✓ |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{2}
\] |
✓ |
✓ |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3}
\] |
✓ |
✓ |
|
|
\[
{}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right )
\] |
✓ |
✓ |
|
|
\[
{}y = x^{2}+2 x y^{\prime }+\frac {{y^{\prime }}^{2}}{2}
\] |
✗ |
✓ |
|
|
\[
{}y^{\prime }-\frac {3 y}{x}+y^{2} x^{3} = 0
\] |
✓ |
✓ |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = a
\] |
✓ |
✓ |
|
|
\[
{}x^{2}-y+\left (x^{2} y^{2}+x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y \left (x -y\right )-x^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{y-x +1}
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (y^{2}-x \right ) y^{\prime }-y+x^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
✓ |
✓ |
|
|
\[
{}3 y^{2} y^{\prime } x +y^{3}-2 x = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right )-y^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x +y} \left (x^{2}+1\right )
\] |
✓ |
✓ |
|
|
\[
{}x^{2} y^{\prime } = 1+y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x y\right )
\] |
✗ |
✗ |
|
|
\[
{}x \left ({\mathrm e}^{y}+4\right ) = {\mathrm e}^{x +y} y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x +y\right )
\] |
✓ |
✓ |
|
|
\[
{}x y^{\prime }+y = x y^{2}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = t \ln \left (y^{2 t}\right )+t^{2}
\] |
✓ |
✗ |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y^{2}-x}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
✗ |
✗ |
|
|
\[
{}x \left (1+y\right )^{2} = \left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y \,{\mathrm e}^{x^{2}} = \sinh \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}y y^{\prime } = 1
\] |
✓ |
✓ |
|
|
\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+3 y = 0
\] |
✓ |
✓ |
|
|
\[
{}5 y^{\prime }-x y = 0
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2} \sqrt {y} = \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+x y {y^{\prime }}^{2} = \ln \left (x \right )
\] |
✗ |
✗ |
|
|
\[
{}2 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 t}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }-2 y = 4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right )
\] |
✓ |
✓ |
|
|
\[
{}10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
✓ |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime }-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
✓ |
✓ |
|
|
\[
{}x y \left (-{y^{\prime }}^{2}+1\right ) = \left (-y^{2}-a^{2}+x^{2}\right ) y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}-x y^{\prime }+y = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}1+y-\left (1-x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2} = 0
\] |
✓ |
✓ |
|
|
\[
{}y-a +x^{2} y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
✓ |
✓ |
|
|
\[
{}1+s^{2}-\sqrt {t}\, s^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = 0
\] |
✓ |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
✓ |
✓ |
|