|
# |
ODE |
Mathematica |
Maple |
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = 2 x \left (t \right )-\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = \frac {9 x \left (t \right )}{5}-y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {5 y \left (t \right )}{4}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -\frac {4 x \left (t \right )}{5}+2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {6 y \left (t \right )}{5}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = a x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+a y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+a y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = a x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = a x \left (t \right )+\frac {5 y \left (t \right )}{4}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = a x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [i^{\prime }\left (t \right ) = \frac {i \left (t \right )}{2}-\frac {v \left (t \right )}{8}, v^{\prime }\left (t \right ) = 2 i \left (t \right )-\frac {v \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {y \left (t \right )}{4}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{4}-\frac {y \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -x \left (t \right )-\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+\frac {3 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}+\frac {y \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {3 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}-y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {y \left (t \right )}{4}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -8 x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+x \left (t \right )^{2}, y^{\prime }\left (t \right ) = y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )^{2} y \left (t \right )-3 x \left (t \right )^{2}-4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) y \left (t \right )^{2}+6 x \left (t \right ) y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )-3 y \left (t \right )+2]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}]
\] |
✗ |
✗ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{4}-\frac {3 x \left (t \right ) y \left (t \right )}{4}\right ]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -\left (x \left (t \right )-y \left (t \right )\right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right ) \left (2+y \left (t \right )\right )]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ) \left (2-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = \left (2+x \left (t \right )\right ) \left (-x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {x \left (t \right )^{3}}{5}-\frac {y \left (t \right )}{5}\right ]
\] |
✗ |
✗ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = x \left (t \right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\frac {3}{4}-y \left (t \right )-\frac {x \left (t \right )}{2}\right )\right ]
\] |
✗ |
✗ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -5 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -9 y_{1} \left (t \right )+5 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 6 y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-4 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 6 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-64 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-14 y_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )-y_{2} \left (t \right )+2 \,{\mathrm e}^{t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )+\sin \left (2 t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-y_{2} \left (t \right )+{\mathrm e}^{-t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+3 y_{2} \left (t \right )+2 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-5 y_{2} \left (t \right )+3, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+3 y_{2} \left (t \right )+5 \cos \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )+\sin \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{3} \left (t \right )-{\mathrm e}^{-t}, y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right )+{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+4 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-5 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}-x_{2} \left (t \right )-\frac {3 x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {3 x_{1} \left (t \right )}{2}-2 x_{2} \left (t \right )-\frac {3 x_{3} \left (t \right )}{2}, x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right )-5 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )-4 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-2 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right )-5 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{3} \left (t \right )-x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right )-2 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+8 x_{2} \left (t \right )+5 x_{3} \left (t \right )+3 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+16 x_{2} \left (t \right )+10 x_{3} \left (t \right )+6 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-14 x_{2} \left (t \right )-11 x_{3} \left (t \right )-3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-8 x_{2} \left (t \right )-5 x_{3} \left (t \right )-3 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-2 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )+2 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+x_{2} \left (t \right )-7 x_{3} \left (t \right )+3 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )+2 x_{4} \left (t \right )+3 x_{5} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{3} \left (t \right )-x_{5} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{4} \left (t \right )-2 x_{5} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )+2 x_{4} \left (t \right )+x_{5} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{2} \left (t \right )-2 x_{3} \left (t \right )+3 x_{4} \left (t \right )+2 x_{5} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )+6 x_{2} \left (t \right )+4 x_{3} \left (t \right )-8 x_{4} \left (t \right )-16 x_{5} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-8 x_{2} \left (t \right )-6 x_{3} \left (t \right )+8 x_{4} \left (t \right )-16 x_{5} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )+7 x_{2} \left (t \right )+4 x_{3} \left (t \right )-9 x_{4} \left (t \right )-16 x_{5} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-5 x_{2} \left (t \right )-3 x_{3} \left (t \right )+5 x_{4} \left (t \right )+7 x_{5} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = \frac {8 x_{2} \left (t \right )}{3}-2 x_{3} \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+6 x_{2} \left (t \right )-6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )+5 x_{2} \left (t \right )-9 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {4 x_{1} \left (t \right )}{3}+\frac {4 x_{2} \left (t \right )}{3}-\frac {11 x_{3} \left (t \right )}{3}, x_{2}^{\prime }\left (t \right ) = -\frac {16 x_{1} \left (t \right )}{3}-\frac {x_{2} \left (t \right )}{3}+\frac {14 x_{3} \left (t \right )}{3}, x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-5 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {3 x_{1} \left (t \right )}{4}+\frac {29 x_{2} \left (t \right )}{4}-\frac {11 x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = -\frac {3 x_{1} \left (t \right )}{4}+\frac {3 x_{2} \left (t \right )}{4}-\frac {5 x_{3} \left (t \right )}{2}, x_{3}^{\prime }\left (t \right ) = \frac {5 x_{1} \left (t \right )}{4}+\frac {11 x_{2} \left (t \right )}{4}-\frac {5 x_{3} \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|