| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [x^{\prime }\left (t \right ) = a \left (b -x \left (t \right )\right )-c f y \left (t \right ), y^{\prime }\left (t \right ) = d \left (x \left (t \right )-y \left (t \right )\right )-c f y \left (t \right )-a y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 17 x \left (t \right )-7 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 12 x \left (t \right )-7 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )-4 y \left (t \right )-z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+3 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )-4 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-8 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right )-8 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+z \left (t \right )-w \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+2 z \left (t \right )+2 w \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+2 w \left (t \right ), w^{\prime }\left (t \right ) = -3 y \left (t \right )-6 z \left (t \right )-6 w \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), z^{\prime }\left (t \right ) = 2 z \left (t \right )+w \left (t \right )+h \left (t \right ), w^{\prime }\left (t \right ) = z \left (t \right )+2 w \left (t \right )+h \left (t \right ), h^{\prime }\left (t \right ) = z \left (t \right )+w \left (t \right )+2 h \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -10 x \left (t \right )+y \left (t \right )+7 z \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+4 y \left (t \right )+5 z \left (t \right ), z^{\prime }\left (t \right ) = -17 x \left (t \right )+y \left (t \right )+12 z \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )-4 y \left (t \right )-z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+3 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )-4 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-8 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right )-8 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -10 x \left (t \right )+y \left (t \right )+7 z \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+4 y \left (t \right )+5 z \left (t \right ), z^{\prime }\left (t \right ) = -17 x \left (t \right )+y \left (t \right )+12 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-5 z \left (t \right ), u^{\prime }\left (t \right ) = 5 z \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )^{2}-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -\sin \left (x \left (t \right )\right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -4 \sin \left (x \left (t \right )\right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = \sin \left (x_{1} \left (t \right )\right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{1} \left (t \right )^{3}]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )+b y \left (t \right ), y^{\prime }\left (t \right ) = c x \left (t \right )+d y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-10 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )-x \left (t \right ) y \left (t \right )]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{2}, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+\left (x \left (t \right )^{2}-y \left (t \right )^{2}\right )^{5}]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+x \left (t \right )^{2}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )+y \left (t \right )^{2}]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-x \left (t \right )^{2}+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = -7 x \left (t \right )-9 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-x \left (t \right )^{2}+2 y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+x \left (t \right )^{2} y \left (t \right )^{2}]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}-x \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{2}]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 3 y \left (t \right )-x \left (t \right )^{2}]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime }\left (x \right ) = -2, z^{\prime }\left (x \right ) = x \,{\mathrm e}^{y \left (x \right )+2 x}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime }\left (x \right )+y \left (x \right ) = {\mathrm e}^{x}, z^{\prime }\left (x \right ) = y \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime }\left (x \right ) = z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y \left (x \right ) y^{\prime }\left (x \right ) = -x, y \left (x \right ) z^{\prime }\left (x \right ) = 2]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [y^{\prime }\left (x \right )+2 z \left (x \right ) = y \left (x \right ), z^{\prime }\left (x \right )+4 y \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|