|
# |
ODE |
Mathematica |
Maple |
Sympy |
|
\[
{} y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} x^{\prime } = -t x
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 y+\cos \left (4 t \right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = t^{2} y^{3}+y^{3}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {\left (t +1\right )^{2}}{\left (1+y\right )^{2}}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 1-y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} y^{\prime } = \frac {t^{2}}{y+t^{3} y}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = y^{2}-2 y+1
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \left (y-2\right ) \left (y+1-\cos \left (t \right )\right )
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right )
\]
|
✗ |
✗ |
✗ |
|
|
\[
{} y^{\prime } = t^{2} y+1+y+t^{2}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = \frac {2 y+1}{t}
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime } = 3-y^{2}
\]
|
✓ |
✓ |
✗ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = 3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 \pi y \left (t \right )-\frac {x \left (t \right )}{3}\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [p^{\prime }\left (t \right ) = 3 p \left (t \right )-2 q \left (t \right )-7 r \left (t \right ), q^{\prime }\left (t \right ) = -2 p \left (t \right )+6 r \left (t \right ), r^{\prime }\left (t \right ) = \frac {73 q \left (t \right )}{100}+2 r \left (t \right )\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 \pi y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = \beta y \left (t \right ), y^{\prime }\left (t \right ) = \gamma x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 1, y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}, y^{\prime }\left (t \right ) = x \left (t \right )-\frac {y \left (t \right )}{2}\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+6 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+6 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = -\frac {9 x \left (t \right )}{10}-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+\frac {11 y \left (t \right )}{10}\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-6 y^{\prime }-7 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} y^{\prime \prime }-y^{\prime }-12 y = 0
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )}{10}, y^{\prime }\left (t \right ) = \frac {z \left (t \right )}{5}, z^{\prime }\left (t \right ) = \frac {2 x \left (t \right )}{5}\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right ), z^{\prime }\left (t \right ) = 2 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 z \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )+z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+2 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), z^{\prime }\left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )-z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = 5 x \left (t \right )-5 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} \left [x^{\prime }\left (t \right ) = -10 x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = 28 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = -\frac {8 z \left (t \right )}{3}\right ]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|