|
# |
ODE |
Solved? |
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=10 y \left (t \right ) \\ y^{\prime }\left (t \right )=-10 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {y \left (t \right )}{2} \\ y^{\prime }\left (t \right )=-8 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=10 x \left (t \right )-7 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=13 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-9 x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 10 x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{3} \left (t \right ) \\ 10 x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ 10 x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+9 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )+2 t \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right )+2 \sin \left (2 t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right )-\cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )=4 x \left (t \right )+5 y \left (t \right ) \\ 2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=3 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} -x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \\ 3 x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right )=x \left (t \right )-15 y \left (t \right )+{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right ) \\ z^{\prime }\left (t \right )=-4 y \left (t \right )+4 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right )+{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right )+3 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=5 x \left (t \right )-y \left (t \right )-t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) t -{\mathrm e}^{t} y \left (t \right )+\cos \left (t \right ) \\ y^{\prime }\left (t \right )={\mathrm e}^{-t} x \left (t \right )+t^{2} y \left (t \right )-\sin \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=5 y \left (t \right )-7 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+t \\ y^{\prime }\left (t \right )=x \left (t \right )-3 z \left (t \right )+t^{2} \\ z^{\prime }\left (t \right )=6 y \left (t \right )-7 z \left (t \right )+t^{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) t -y \left (t \right )+{\mathrm e}^{t} z \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+t^{2} y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )={\mathrm e}^{-t} x \left (t \right )+3 t y \left (t \right )+t^{3} z \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=4 x_{1} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+x_{3} \left (t \right )+1 \\ x_{2}^{\prime }\left (t \right )=x_{3} \left (t \right )+x_{4} \left (t \right )+t \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{4} \left (t \right )+t^{2} \\ x_{4}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+t^{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-8 x_{1} \left (t \right )-11 x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-6 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-12 x_{2} \left (t \right )-x_{3} \left (t \right )-6 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-4 x_{2} \left (t \right )-x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=7 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-50 x_{1} \left (t \right )+20 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=100 x_{1} \left (t \right )-60 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+4 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-6 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-6 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=9 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-9 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=4 x_{3} \left (t \right )+4 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+9 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{3} \left (t \right )+8 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-21 x_{1} \left (t \right )-5 x_{2} \left (t \right )-27 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-21 x_{3} \left (t \right )-2 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+7 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+4 x_{2} \left (t \right )+10 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+10 x_{2} \left (t \right )+4 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=7 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+4 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right )+3 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=5 x \left (t \right )-y \left (t \right )-t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=4 x_{1} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+x_{3} \left (t \right )+1 \\ x_{2}^{\prime }\left (t \right )=x_{3} \left (t \right )+x_{4} \left (t \right )+t \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{4} \left (t \right )+t^{2} \\ x_{4}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+t^{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=6 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=7 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-50 x_{1} \left (t \right )+20 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=100 x_{1} \left (t \right )-60 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+4 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-6 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-6 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=9 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-9 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=4 x_{3} \left (t \right )+4 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+9 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{3} \left (t \right )+8 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-21 x_{1} \left (t \right )-5 x_{2} \left (t \right )-27 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-21 x_{3} \left (t \right )-2 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+7 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+4 x_{2} \left (t \right )+10 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+10 x_{2} \left (t \right )+4 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=7 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+4 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-40 x_{1} \left (t \right )-12 x_{2} \left (t \right )+54 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=35 x_{1} \left (t \right )+13 x_{2} \left (t \right )-46 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-25 x_{1} \left (t \right )-7 x_{2} \left (t \right )+34 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-20 x_{1} \left (t \right )+11 x_{2} \left (t \right )+13 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=12 x_{1} \left (t \right )-x_{2} \left (t \right )-7 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-48 x_{1} \left (t \right )+21 x_{2} \left (t \right )+31 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=147 x_{1} \left (t \right )+23 x_{2} \left (t \right )-202 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-90 x_{1} \left (t \right )-9 x_{2} \left (t \right )+129 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=90 x_{1} \left (t \right )+15 x_{2} \left (t \right )-123 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )-7 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-12 x_{1} \left (t \right )+7 x_{2} \left (t \right )+11 x_{3} \left (t \right )+9 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=24 x_{1} \left (t \right )-17 x_{2} \left (t \right )-19 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-18 x_{1} \left (t \right )+13 x_{2} \left (t \right )+17 x_{3} \left (t \right )+9 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=13 x_{1} \left (t \right )-42 x_{2} \left (t \right )+106 x_{3} \left (t \right )+139 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-16 x_{2} \left (t \right )+52 x_{3} \left (t \right )+70 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+6 x_{2} \left (t \right )-20 x_{3} \left (t \right )-31 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-x_{1} \left (t \right )-6 x_{2} \left (t \right )+22 x_{3} \left (t \right )+33 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=23 x_{1} \left (t \right )-18 x_{2} \left (t \right )-16 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-8 x_{1} \left (t \right )+6 x_{2} \left (t \right )+7 x_{3} \left (t \right )+9 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=34 x_{1} \left (t \right )-27 x_{2} \left (t \right )-26 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-26 x_{1} \left (t \right )+21 x_{2} \left (t \right )+25 x_{3} \left (t \right )+12 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=47 x_{1} \left (t \right )-8 x_{2} \left (t \right )+5 x_{3} \left (t \right )-5 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-10 x_{1} \left (t \right )+32 x_{2} \left (t \right )+18 x_{3} \left (t \right )-2 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=139 x_{1} \left (t \right )-40 x_{2} \left (t \right )-167 x_{3} \left (t \right )-121 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-232 x_{1} \left (t \right )+64 x_{2} \left (t \right )+360 x_{3} \left (t \right )+248 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=139 x_{1} \left (t \right )-14 x_{2} \left (t \right )-52 x_{3} \left (t \right )-14 x_{4} \left (t \right )+28 x_{5} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-22 x_{1} \left (t \right )+5 x_{2} \left (t \right )+7 x_{3} \left (t \right )+8 x_{4} \left (t \right )-7 x_{5} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=370 x_{1} \left (t \right )-38 x_{2} \left (t \right )-139 x_{3} \left (t \right )-38 x_{4} \left (t \right )+76 x_{5} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=152 x_{1} \left (t \right )-16 x_{2} \left (t \right )-59 x_{3} \left (t \right )-13 x_{4} \left (t \right )+35 x_{5} \left (t \right ) \\ x_{5}^{\prime }\left (t \right )=95 x_{1} \left (t \right )-10 x_{2} \left (t \right )-38 x_{3} \left (t \right )-7 x_{4} \left (t \right )+23 x_{5} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+13 x_{2} \left (t \right )-13 x_{6} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-14 x_{1} \left (t \right )+19 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )+4 x_{6} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-30 x_{1} \left (t \right )+12 x_{2} \left (t \right )-7 x_{3} \left (t \right )-30 x_{4} \left (t \right )+12 x_{5} \left (t \right )+18 x_{6} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-10 x_{3} \left (t \right )-9 x_{4} \left (t \right )+10 x_{5} \left (t \right )+2 x_{6} \left (t \right ) \\ x_{5}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+6 x_{4} \left (t \right )+5 x_{5} \left (t \right )-15 x_{6} \left (t \right ) \\ x_{6}^{\prime }\left (t \right )=-14 x_{1} \left (t \right )+23 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=9 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-6 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+7 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-7 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )-3 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=7 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+9 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-7 x_{1} \left (t \right )+9 x_{2} \left (t \right )+7 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=25 x_{1} \left (t \right )+12 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-18 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+13 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-19 x_{1} \left (t \right )+12 x_{2} \left (t \right )+84 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-8 x_{1} \left (t \right )+4 x_{2} \left (t \right )+33 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-13 x_{1} \left (t \right )+40 x_{2} \left (t \right )-48 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-8 x_{1} \left (t \right )+23 x_{2} \left (t \right )-24 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )-4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right )-4 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )-3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+4 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=18 x_{1} \left (t \right )+7 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-27 x_{1} \left (t \right )-9 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-4 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-12 x_{2} \left (t \right )-x_{3} \left (t \right )-6 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-4 x_{2} \left (t \right )-x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=2 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=x_{2} \left (t \right )+x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+7 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right )-4 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-6 x_{2} \left (t \right )-14 x_{3} \left (t \right )+x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=39 x_{1} \left (t \right )+8 x_{2} \left (t \right )-16 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-36 x_{1} \left (t \right )-5 x_{2} \left (t \right )+16 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=72 x_{1} \left (t \right )+16 x_{2} \left (t \right )-29 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=28 x_{1} \left (t \right )+50 x_{2} \left (t \right )+100 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=15 x_{1} \left (t \right )+33 x_{2} \left (t \right )+60 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-15 x_{1} \left (t \right )-30 x_{2} \left (t \right )-57 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+17 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=8 x_{1} \left (t \right )-8 x_{2} \left (t \right )+10 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-15 x_{1} \left (t \right )-7 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=34 x_{1} \left (t \right )+16 x_{2} \left (t \right )-11 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=17 x_{1} \left (t \right )+7 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )-2 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=7 x_{1} \left (t \right )-4 x_{2} \left (t \right )-6 x_{3} \left (t \right )+11 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )+3 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )+6 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )+x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{2} \left (t \right )-5 x_{3} \left (t \right )+3 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-13 x_{2} \left (t \right )+22 x_{3} \left (t \right )-12 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-27 x_{2} \left (t \right )+45 x_{3} \left (t \right )-25 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=35 x_{1} \left (t \right )-12 x_{2} \left (t \right )+4 x_{3} \left (t \right )+30 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=22 x_{1} \left (t \right )-8 x_{2} \left (t \right )+3 x_{3} \left (t \right )+19 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-10 x_{1} \left (t \right )+3 x_{2} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-27 x_{1} \left (t \right )+9 x_{2} \left (t \right )-3 x_{3} \left (t \right )-23 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=11 x_{1} \left (t \right )-x_{2} \left (t \right )+26 x_{3} \left (t \right )+6 x_{4} \left (t \right )-3 x_{5} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-9 x_{1} \left (t \right )-24 x_{3} \left (t \right )-6 x_{4} \left (t \right )+3 x_{5} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+9 x_{3} \left (t \right )+5 x_{4} \left (t \right )-x_{5} \left (t \right ) \\ x_{5}^{\prime }\left (t \right )=-48 x_{1} \left (t \right )-3 x_{2} \left (t \right )-138 x_{3} \left (t \right )-30 x_{4} \left (t \right )+18 x_{5} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{3} \left (t \right )-4 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=4 x_{3} \left (t \right )+3 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-8 x_{3} \left (t \right )-3 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-18 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-25 x_{3} \left (t \right )-9 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=33 x_{1} \left (t \right )+10 x_{2} \left (t \right )+90 x_{3} \left (t \right )+32 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{10}+\frac {3 x_{2} \left (t \right )}{40} \\ x_{2}^{\prime }\left (t \right )=\frac {x_{1} \left (t \right )}{10}-\frac {x_{2} \left (t \right )}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=\frac {9 x_{1} \left (t \right )}{5}-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=\frac {3 x_{1} \left (t \right )}{4}-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {4 x_{1} \left (t \right )}{5}+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+\frac {6 x_{2} \left (t \right )}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{4}+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{4} \\ x_{3}^{\prime }\left (t \right )=-\frac {x_{3} \left (t \right )}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{4}+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{4} \\ x_{3}^{\prime }\left (t \right )=\frac {x_{3} \left (t \right )}{10} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{2}-\frac {x_{2} \left (t \right )}{8} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=8 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {3 x_{1} \left (t \right )}{2}+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{4}-\frac {x_{2} \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+\frac {5 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=-\frac {5 x_{1} \left (t \right )}{2}+2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {5 x_{1} \left (t \right )}{2}+\frac {3 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=-\frac {3 x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+\frac {3 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=-\frac {3 x_{1} \left (t \right )}{2}-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+9 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+6 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {5 x_{1} \left (t \right )}{2}+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2}+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-\frac {5 x_{3} \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+\sqrt {3}\, x_{2} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=\sqrt {3}\, x_{1} \left (t \right )-x_{2} \left (t \right )+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )-\cos \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+\frac {1}{t^{3}} \\ x_{2}^{\prime }\left (t \right )=8 x_{1} \left (t \right )-4 x_{2} \left (t \right )-\frac {1}{t^{2}} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+\frac {1}{t} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )+\frac {2}{t}+4 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {5 x_{1} \left (t \right )}{4}+\frac {3 x_{2} \left (t \right )}{4}+2 t \\ x_{2}^{\prime }\left (t \right )=\frac {3 x_{1} \left (t \right )}{4}-\frac {5 x_{2} \left (t \right )}{4}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+\sqrt {2}\, x_{2} \left (t \right )+{\mathrm e}^{-t} \\ x_{2}^{\prime }\left (t \right )=\sqrt {2}\, x_{1} \left (t \right )-2 x_{2} \left (t \right )-{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\csc \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sec \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-\frac {x_{1} \left (t \right )}{2}-\frac {x_{2} \left (t \right )}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-\frac {5 x_{2} \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-5 x_{1} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2} \\ x_{2}^{\prime }\left (t \right )=\frac {9 x_{1} \left (t \right )}{5}-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-2 \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right )-1 \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{2} \left (t \right )+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )+2 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-\frac {5 y_{1} \left (t \right )}{4}+\frac {3 y_{2} \left (t \right )}{4} \\ y_{2}^{\prime }\left (t \right )=\frac {3 y_{1} \left (t \right )}{4}-\frac {5 y_{2} \left (t \right )}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-\frac {4 y_{1} \left (t \right )}{5}+\frac {3 y_{2} \left (t \right )}{5} \\ y_{2}^{\prime }\left (t \right )=-\frac {2 y_{1} \left (t \right )}{5}-\frac {11 y_{2} \left (t \right )}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )-4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-3 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )-3 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-2 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-2 y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-8 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-8 y_{1} \left (t \right )-4 y_{2} \left (t \right )-6 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+8 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=12 y_{1} \left (t \right )-4 y_{2} \left (t \right )+10 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )+y_{2} \left (t \right )-7 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-3 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )-6 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+6 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )-2 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+2 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+7 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-10 y_{1} \left (t \right )+10 y_{2} \left (t \right )-5 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )+7 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-2 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )+4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )-11 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )+y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )+12 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-8 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-10 y_{1} \left (t \right )+9 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+2 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-13 y_{1} \left (t \right )+16 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-9 y_{1} \left (t \right )+11 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=2 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=4 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=\frac {y_{1} \left (t \right )}{3}+\frac {y_{2} \left (t \right )}{3}-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-\frac {4 y_{1} \left (t \right )}{3}-\frac {4 y_{2} \left (t \right )}{3}+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-\frac {2 y_{1} \left (t \right )}{3}+\frac {y_{2} \left (t \right )}{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-y_{1} \left (t \right )+3 y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-2 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+3 y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right )+3 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=6 y_{1} \left (t \right )-5 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right )+3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-11 y_{1} \left (t \right )+8 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )-3 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=15 y_{1} \left (t \right )-9 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=16 y_{1} \left (t \right )-9 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-7 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )+24 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )+17 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )+3 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )+y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )+3 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )-4 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-9 y_{1} \left (t \right )-5 y_{2} \left (t \right )+6 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )-4 y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=3 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-2 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-8 y_{2} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right )+9 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-5 y_{1} \left (t \right )-y_{2} \left (t \right )+11 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-7 y_{1} \left (t \right )+y_{2} \left (t \right )+13 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+8 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=5 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )+9 y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )+10 y_{2} \left (t \right )-12 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right )+6 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=2 y_{2} \left (t \right )-2 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )+5 y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-2 y_{1} \left (t \right )-12 y_{2} \left (t \right )+10 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-24 y_{2} \left (t \right )+11 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )-24 y_{2} \left (t \right )+8 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )-12 y_{2} \left (t \right )+8 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-9 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )-6 y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-y_{1} \left (t \right )-3 y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )-2 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-3 y_{2} \left (t \right )+4 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=4 y_{1} \left (t \right )+5 y_{2} \left (t \right )-8 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+3 y_{2} \left (t \right )-5 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-y_{2} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-y_{1} \left (t \right )+2 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-5 y_{1} \left (t \right )+5 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-11 y_{1} \left (t \right )+4 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-26 y_{1} \left (t \right )+9 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=y_{1} \left (t \right )+2 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=-4 y_{1} \left (t \right )+5 y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=5 y_{1} \left (t \right )-6 y_{2} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=3 y_{1} \left (t \right )-y_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )-3 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=2 y_{2} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=5 y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{1} \left (t \right )-5 y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )+7 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=2 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=y_{2} \left (t \right )+y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=y_{1} \left (t \right )+y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (t \right )=-3 y_{1} \left (t \right )+y_{2} \left (t \right )-3 y_{3} \left (t \right ) \\ y_{2}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right ) \\ y_{3}^{\prime }\left (t \right )=4 y_{1} \left (t \right )-2 y_{2} \left (t \right )+3 y_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right )+t \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+3 y \left (t \right )-1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+5 y \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-5 y \left (t \right )+\sin \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right )+\tan \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+\textit {f\_1} \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+f_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=6 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=7 x_{1} \left (t \right )-x_{2} \left (t \right )+6 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-10 x_{1} \left (t \right )+4 x_{2} \left (t \right )-12 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-7 x_{1} \left (t \right )+6 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=6 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+6 x_{4} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+6 x_{2} \left (t \right )+9 x_{3} \left (t \right )+18 x_{4} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+10 x_{2} \left (t \right )+15 x_{3} \left (t \right )+30 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=7 x_{1} \left (t \right )+14 x_{2} \left (t \right )+21 x_{3} \left (t \right )+42 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+10 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-x_{2} \left (t \right )-2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )-3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-5 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-3 x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-x_{3} \left (t \right )+2 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=10 x_{1} \left (t \right )+9 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=-4 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=2 x_{3} \left (t \right )+3 x_{4} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+{\mathrm e}^{c t} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\sin \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\tan \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{2} \left (t \right )+f_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+f_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{2 t} \\ x_{2}^{\prime }\left (t \right )=2 x_{2} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{3 t} \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )-t^{2} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+\sin \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+{\mathrm e}^{t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )-x_{2} \left (t \right )+1 \\ x_{2}^{\prime }\left (t \right )=-4 x_{2} \left (t \right )-x_{3} \left (t \right )+t \\ x_{3}^{\prime }\left (t \right )=5 x_{2} \left (t \right )+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{2 t} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-4 x_{3} \left (t \right )+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{3} \left (t \right )+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{3 t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )-{\mathrm e}^{3 t} \\ x_{3}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )-{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{8 t} \\ x_{3}^{\prime }\left (t \right )=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+2 \,{\mathrm e}^{8 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )=\cos \left (t \right ) \\ y^{\prime }\left (t \right )+y \left (t \right )=4 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+5 x \left (t \right )=3 t^{2} \\ y^{\prime }\left (t \right )+y \left (t \right )={\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 x \left (t \right )=3 t \\ x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )+y \left (t \right )=\cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right )=2 \sin \left (t \right ) \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=3 y \left (t \right )-3 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right )={\mathrm e}^{t} \\ 5 x \left (t \right )-3 y^{\prime }\left (t \right )=y \left (t \right )+2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 5 y^{\prime }\left (t \right )-3 x^{\prime }\left (t \right )-5 y \left (t \right )=5 t \\ 3 x^{\prime }\left (t \right )-5 y^{\prime }\left (t \right )-2 x \left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right ) \\ z^{\prime }\left (t \right )=3 y \left (t \right )-2 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+y \left (t \right )=-{\mathrm e}^{t} \\ x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )=t \\ 5 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )=t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+x \left (t \right )+2 y^{\prime }\left (t \right )+7 y \left (t \right )={\mathrm e}^{t}+2 \\ -2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )={\mathrm e}^{t}-1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )={\mathrm e}^{-t}-1 \\ x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )={\mathrm e}^{2 t}+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right )=1+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )+2 y \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right )={\mathrm e}^{t}+2 \\ x^{\prime }\left (t \right )-x \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right )=3+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-18 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=5 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=16 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-18 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+3 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-18 x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=3 x_{1} \left (t \right )-x_{2} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-8 \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )-8 \\ x_{2}^{\prime }\left (t \right )=x_{1} \left (t \right )+x_{2} \left (t \right )+3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=6 y_{1} \left (x \right )+y_{2} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right )+{\mathrm e}^{3 x} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=3 y_{1} \left (x \right )+x y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=2 x y_{1} \left (x \right )-y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+t -1 \\ y^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right )-5 t -2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right )-6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )+6 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-5 t +2 \\ y^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right )-8 t -8 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-7 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+\sqrt {2}\, y \left (t \right ) \\ y^{\prime }\left (t \right )=\sqrt {2}\, x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-6 x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right )+3 z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ) \\ z^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-4 t +1 \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right )+3 t +4 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right )-t +3 \\ y^{\prime }\left (t \right )=x \left (t \right )+4 y \left (t \right )+t -2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right )-t +3 \\ y^{\prime }\left (t \right )=-x \left (t \right )-5 y \left (t \right )+t +1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) y \left (t \right )+1 \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=t y \left (t \right )+1 \\ y^{\prime }\left (t \right )=-x \left (t \right ) t +y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+8 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-7 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right )-9 z \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=10 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right )-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+z \left (t \right )+t -1 \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )-z \left (t \right )-3 t^{2} \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+z \left (t \right )+t^{2}-t +2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )+5 y \left (t \right )-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{5 t} \\ z^{\prime }\left (t \right )=-2 y \left (t \right )+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t \\ y^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t \\ z^{\prime }\left (t \right )=-2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-7 y \left (t \right )+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-7 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+\frac {y \left (t \right )}{4} \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ z^{\prime }\left (t \right )=-2 x \left (t \right )-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-\frac {5 x \left (t \right )}{2}+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {5 x \left (t \right )}{2}+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {3 x \left (t \right )}{4}-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=10 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right )-12 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-6 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right )-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-7 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+10 y \left (t \right )+4 z \left (t \right ) \\ z^{\prime }\left (t \right )=5 y \left (t \right )+2 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=3 y \left (t \right )-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ) \\ z^{\prime }\left (t \right )=\frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ) \\ z^{\prime }\left (t \right )=\frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right )+2 z \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right )-2 z \left (t \right ) \\ z^{\prime }\left (t \right )=6 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {x \left (t \right )}{2} \\ y^{\prime }\left (t \right )=x \left (t \right )-\frac {y \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+4 z \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {9 x \left (t \right )}{10}+\frac {21 y \left (t \right )}{10}+\frac {16 z \left (t \right )}{5} \\ y^{\prime }\left (t \right )=\frac {7 x \left (t \right )}{10}+\frac {13 y \left (t \right )}{2}+\frac {21 z \left (t \right )}{5} \\ z^{\prime }\left (t \right )=\frac {11 x \left (t \right )}{10}+\frac {17 y \left (t \right )}{10}+\frac {17 z \left (t \right )}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5} \\ x_{2}^{\prime }\left (t \right )=\frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right ) \\ x_{3}^{\prime }\left (t \right )=x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right ) \\ x_{5}^{\prime }\left (t \right )=-\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=9 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-6 x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-5 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=12 x \left (t \right )-9 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=2 y \left (t \right )+5 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=3 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=4 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=4 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=z \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-8 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=z \left (t \right ) \\ y^{\prime }\left (t \right )=-z \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+6 z \left (t \right ) \\ z^{\prime }\left (t \right )=-4 x \left (t \right )-3 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-12 y \left (t \right )-14 z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-3 z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-2 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )-7 \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+9 y \left (t \right )+2 \\ y^{\prime }\left (t \right )=-x \left (t \right )+11 y \left (t \right )+6 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right )+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )-7 y \left (t \right )+10 \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right )-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=9 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-6 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+7 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )+2 t +1 \\ y^{\prime }\left (t \right )=5 x \left (t \right )+y \left (t \right )+3 t -1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=y \left (t \right )+t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=y \left (t \right )+t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=y \left (t \right )+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=a x \left (t \right ) \\ y^{\prime }\left (t \right )=b \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=a y \left (t \right ) \\ y^{\prime }\left (t \right )=-a x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=a y \left (t \right ) \\ y^{\prime }\left (t \right )=b x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=a x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+a y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=a x \left (t \right )+b y \left (t \right ) \\ y^{\prime }\left (t \right )=c x \left (t \right )+b y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }\left (t \right )+b y^{\prime }\left (t \right )=\alpha x \left (t \right )+\beta y \left (t \right ) \\ b x^{\prime }\left (t \right )-a y^{\prime }\left (t \right )=\beta x \left (t \right )-\alpha y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right )=0 \\ y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-7 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1} \\ y^{\prime }\left (t \right )=a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 y \left (t \right )=3 t \\ y^{\prime }\left (t \right )-2 x \left (t \right )=4 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y \left (t \right )-t^{2}+6 t +1=0 \\ y^{\prime }\left (t \right )-x \left (t \right )=-3 t^{2}+3 t +1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right )={\mathrm e}^{2 t} \\ y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right )={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )={\mathrm e}^{2 t}+t \\ x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right )={\mathrm e}^{t}-1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )={\mathrm e}^{t} \\ 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right )=\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right )={\mathrm e}^{t} \\ 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right )=3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right )={\mathrm e}^{t} \\ 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right )=t \\ 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right )={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) f \left (t \right )+y \left (t \right ) g \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) g \left (t \right )+y \left (t \right ) f \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+\left (a x \left (t \right )+b y \left (t \right )\right ) f \left (t \right )=g \left (t \right ) \\ y^{\prime }\left (t \right )+\left (c x \left (t \right )+d y \left (t \right )\right ) f \left (t \right )=h \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \cos \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) {\mathrm e}^{-\sin \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }\left (t \right )+y \left (t \right )=0 \\ t y^{\prime }\left (t \right )+x \left (t \right )=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )=t \\ t y^{\prime }\left (t \right )-\left (t +2\right ) x \left (t \right )-t y \left (t \right )=-t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )-2 y \left (t \right )=t \\ t y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right )=t^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }\left (t \right )=t \left (1-2 \sin \left (t \right )\right ) x \left (t \right )+t^{2} y \left (t \right ) \\ t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }\left (t \right )=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x \left (t \right )+t \left (1-t \cos \left (t \right )\right ) y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )=f \left (t \right ) \\ x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )=g \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )=0 \\ x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+x \left (t \right )=2 t \\ x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )-9 x \left (t \right )+3 y \left (t \right )=\sin \left (2 t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right )=0 \\ x^{\prime \prime }\left (t \right )-2 y^{\prime }\left (t \right )=2 t -\cos \left (2 t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }\left (t \right )-t y^{\prime }\left (t \right )-2 y \left (t \right )=0 \\ t x^{\prime \prime }\left (t \right )+2 x^{\prime }\left (t \right )+x \left (t \right ) t =0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+a y \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )-a^{2} y \left (t \right )=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=a x \left (t \right )+b y \left (t \right ) \\ y^{\prime \prime }\left (t \right )=c x \left (t \right )+d y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1} \\ y^{\prime \prime }\left (t \right )=a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+x \left (t \right )+y \left (t \right )=-5 \\ y^{\prime \prime }\left (t \right )-4 x \left (t \right )-3 y \left (t \right )=-3 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x \left (t \right )+\frac {3 c^{2} y \left (t \right ) \sin \left (2 a t b \right )}{2} \\ y^{\prime \prime }\left (t \right )=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y \left (t \right )+\frac {3 c^{2} x \left (t \right ) \sin \left (2 a t b \right )}{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+6 x \left (t \right )+7 y \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right )=2 t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-a y^{\prime }\left (t \right )+b x \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )+a x^{\prime }\left (t \right )+b y \left (t \right )=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} a_{1} x^{\prime \prime }\left (t \right )+b_{1} x^{\prime }\left (t \right )+c_{1} x \left (t \right )-A y^{\prime }\left (t \right )=B \,{\mathrm e}^{i \omega t} \\ a_{2} y^{\prime \prime }\left (t \right )+b_{2} y^{\prime }\left (t \right )+c_{2} y \left (t \right )+A x^{\prime }\left (t \right )=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+a \left (x^{\prime }\left (t \right )-y^{\prime }\left (t \right )\right )+b_{1} x \left (t \right )=c_{1} {\mathrm e}^{i \omega t} \\ y^{\prime \prime }\left (t \right )+a \left (y^{\prime }\left (t \right )-x^{\prime }\left (t \right )\right )+b_{2} y \left (t \right )=c_{2} {\mathrm e}^{i \omega t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} \operatorname {a11} x^{\prime \prime }\left (t \right )+\operatorname {b11} x^{\prime }\left (t \right )+\operatorname {c11} x \left (t \right )+\operatorname {a12} y^{\prime \prime }\left (t \right )+\operatorname {b12} y^{\prime }\left (t \right )+\operatorname {c12} y \left (t \right )=0 \\ \operatorname {a21} x^{\prime \prime }\left (t \right )+\operatorname {b21} x^{\prime }\left (t \right )+\operatorname {c21} x \left (t \right )+\operatorname {a22} y^{\prime \prime }\left (t \right )+\operatorname {b22} y^{\prime }\left (t \right )+\operatorname {c22} y \left (t \right )=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+y \left (t \right )=0 \\ y^{\prime \prime \prime }\left (t \right )-y^{\prime \prime }\left (t \right )+2 x^{\prime }\left (t \right )-x \left (t \right )=t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )=\sinh \left (2 t \right ) \\ 2 x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )=2 t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=0 \\ x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )-x \left (t \right )=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=2 y \left (t \right )+3 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-y \left (t \right )+z \left (t \right )=0 \\ y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=t \\ z^{\prime }\left (t \right )-x \left (t \right )-z \left (t \right )=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }\left (t \right )=b c \left (y \left (t \right )-z \left (t \right )\right ) \\ b y^{\prime }\left (t \right )=c a \left (z \left (t \right )-x \left (t \right )\right ) \\ c z^{\prime }\left (t \right )=a b \left (x \left (t \right )-y \left (t \right )\right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=c y \left (t \right )-b z \left (t \right ) \\ y^{\prime }\left (t \right )=a z \left (t \right )-c x \left (t \right ) \\ z^{\prime }\left (t \right )=b x \left (t \right )-a y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=h \left (t \right ) y \left (t \right )-g \left (t \right ) z \left (t \right ) \\ y^{\prime }\left (t \right )=f \left (t \right ) z \left (t \right )-h \left (t \right ) x \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right ) g \left (t \right )-y \left (t \right ) f \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right )-x \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+48 y \left (t \right )-28 z \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+40 y \left (t \right )-22 z \left (t \right ) \\ z^{\prime }\left (t \right )=-6 x \left (t \right )+57 y \left (t \right )-31 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )-72 y \left (t \right )+44 z \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-4 y \left (t \right )+26 z \left (t \right ) \\ z^{\prime }\left (t \right )=6 x \left (t \right )-63 y \left (t \right )+38 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=a x \left (t \right )+g y \left (t \right )+\beta z \left (t \right ) \\ y^{\prime }\left (t \right )=g x \left (t \right )+b y \left (t \right )+\alpha z \left (t \right ) \\ z^{\prime }\left (t \right )=\beta x \left (t \right )+\alpha y \left (t \right )+c z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }\left (t \right )=2 x \left (t \right )-t \\ t^{3} y^{\prime }\left (t \right )=-x \left (t \right )+t^{2} y \left (t \right )+t \\ t^{4} z^{\prime }\left (t \right )=-x \left (t \right )-t^{2} y \left (t \right )+t^{3} z \left (t \right )+t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} a t x^{\prime }\left (t \right )=b c \left (y \left (t \right )-z \left (t \right )\right ) \\ b t y^{\prime }\left (t \right )=c a \left (z \left (t \right )-x \left (t \right )\right ) \\ c t z^{\prime }\left (t \right )=a b \left (x \left (t \right )-y \left (t \right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=a x_{2} \left (t \right )+b x_{3} \left (t \right ) \cos \left (c t \right )+b x_{4} \left (t \right ) \sin \left (c t \right ) \\ x_{2}^{\prime }\left (t \right )=-a x_{1} \left (t \right )+b x_{3} \left (t \right ) \sin \left (c t \right )-b x_{4} \left (t \right ) \cos \left (c t \right ) \\ x_{3}^{\prime }\left (t \right )=-b x_{1} \left (t \right ) \cos \left (c t \right )-b x_{2} \left (t \right ) \sin \left (c t \right )+a x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-b x_{1} \left (t \right ) \sin \left (c t \right )+b x_{2} \left (t \right ) \cos \left (c t \right )-a x_{3} \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \left (x \left (t \right )+y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (x \left (t \right )+y \left (t \right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\left (a y \left (t \right )+b \right ) x \left (t \right ) \\ y^{\prime }\left (t \right )=\left (c x \left (t \right )+d \right ) y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (a \left (p x \left (t \right )+q y \left (t \right )\right )+\alpha \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (\beta +b \left (p x \left (t \right )+q y \left (t \right )\right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=h \left (a -x \left (t \right )\right ) \left (c -x \left (t \right )-y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=k \left (b -y \left (t \right )\right ) \left (c -x \left (t \right )-y \left (t \right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )^{2}-\cos \left (x \left (t \right )\right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \sin \left (x \left (t \right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )^{2} y \left (t \right )-x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right )+x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=\left \{\begin {array}{cc} x \left (t \right )^{2}+y \left (t \right )^{2} & 2 x \left (t \right )\le x \left (t \right )^{2}+y \left (t \right )^{2} \\ \left (\frac {x \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{2 x \left (t \right )}\right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) & \operatorname {otherwise} \end {array}\right . \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right )+\left (\left \{\begin {array}{cc} x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) & x \left (t \right )^{2}+y \left (t \right )^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+\left (\left \{\begin {array}{cc} y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right ) \sin \left (\frac {1}{x \left (t \right )^{2}+y \left (t \right )^{2}}\right ) & x \left (t \right )^{2}+y \left (t \right )^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} \left (t^{2}+1\right ) x^{\prime }\left (t \right )=-x \left (t \right ) t +y \left (t \right ) \\ \left (t^{2}+1\right ) y^{\prime }\left (t \right )=-x \left (t \right )-t y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} \left (x \left (t \right )^{2}+y \left (t \right )^{2}-t^{2}\right ) x^{\prime }\left (t \right )=-2 x \left (t \right ) t \\ \left (x \left (t \right )^{2}+y \left (t \right )^{2}-t^{2}\right ) y^{\prime }\left (t \right )=-2 t y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} {x^{\prime }\left (t \right )}^{2}+t x^{\prime }\left (t \right )+a y^{\prime }\left (t \right )-x \left (t \right )=0 \\ x^{\prime }\left (t \right ) y^{\prime }\left (t \right )+t y^{\prime }\left (t \right )-y \left (t \right )=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x \left (t \right )=t x^{\prime }\left (t \right )+f \left (x^{\prime }\left (t \right ), y^{\prime }\left (t \right )\right ) \\ y \left (t \right )=t y^{\prime }\left (t \right )+g \left (x^{\prime }\left (t \right ), y^{\prime }\left (t \right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=a \,{\mathrm e}^{2 x \left (t \right )}-{\mathrm e}^{-x \left (t \right )}+{\mathrm e}^{-2 x \left (t \right )} \cos \left (y \left (t \right )\right )^{2} \\ y^{\prime \prime }\left (t \right )={\mathrm e}^{-2 x \left (t \right )} \sin \left (y \left (t \right )\right ) \cos \left (y \left (t \right )\right )-\frac {\sin \left (y \left (t \right )\right )}{\cos \left (y \left (t \right )\right )^{3}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=\frac {k x \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{{3}/{2}}} \\ y^{\prime \prime }\left (t \right )=\frac {k y \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{{3}/{2}}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )^{2}+z \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }\left (t \right )=\left (b -c \right ) y \left (t \right ) z \left (t \right ) \\ b y^{\prime }\left (t \right )=\left (c -a \right ) z \left (t \right ) x \left (t \right ) \\ c z^{\prime }\left (t \right )=\left (a -b \right ) x \left (t \right ) y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (y \left (t \right )-z \left (t \right )\right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (z \left (t \right )-x \left (t \right )\right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \left (x \left (t \right )-y \left (t \right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=x \left (t \right ) y \left (t \right ) \\ y^{\prime }\left (t \right )+z^{\prime }\left (t \right )=y \left (t \right ) z \left (t \right ) \\ x^{\prime }\left (t \right )+z^{\prime }\left (t \right )=x \left (t \right ) z \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {x \left (t \right )^{2}}{2}-\frac {y \left (t \right )}{24} \\ y^{\prime }\left (t \right )=2 x \left (t \right ) y \left (t \right )-3 z \left (t \right ) \\ z^{\prime }\left (t \right )=3 x \left (t \right ) z \left (t \right )-\frac {y \left (t \right )^{2}}{6} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (z \left (t \right )^{2}-x \left (t \right )^{2}\right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \left (x \left (t \right )^{2}-y \left (t \right )^{2}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \left (z \left (t \right )^{2}+x \left (t \right )^{2}\right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )^{2} y \left (t \right )-x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right )^{2}-x \left (t \right )^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} \left (x \left (t \right )-y \left (t \right )\right ) \left (x \left (t \right )-z \left (t \right )\right ) x^{\prime }\left (t \right )=f \left (t \right ) \\ \left (-x \left (t \right )+y \left (t \right )\right ) \left (y \left (t \right )-z \left (t \right )\right ) y^{\prime }\left (t \right )=f \left (t \right ) \\ \left (z \left (t \right )-x \left (t \right )\right ) \left (z \left (t \right )-y \left (t \right )\right ) z^{\prime }\left (t \right )=f \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right ) \sin \left (x_{2} \left (t \right )\right )=x_{4} \left (t \right ) \sin \left (x_{3} \left (t \right )\right )+x_{5} \left (t \right ) \cos \left (x_{3} \left (t \right )\right ) \\ x_{2}^{\prime }\left (t \right )=x_{4} \left (t \right ) \cos \left (x_{3} \left (t \right )\right )-x_{5} \left (t \right ) \sin \left (x_{3} \left (t \right )\right ) \\ x_{3}^{\prime }\left (t \right )+x_{1}^{\prime }\left (t \right ) \cos \left (x_{2} \left (t \right )\right )=a \\ x_{4}^{\prime }\left (t \right )-\left (1-\lambda \right ) a x_{5} \left (t \right )=-m \sin \left (x_{2} \left (t \right )\right ) \cos \left (x_{3} \left (t \right )\right ) \\ x_{5}^{\prime }\left (t \right )+\left (1-\lambda \right ) a x_{4} \left (t \right )=m \sin \left (x_{2} \left (t \right )\right ) \sin \left (x_{3} \left (t \right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right )={\mathrm e}^{t} \\ 4 x \left (t \right )-3 y^{\prime }\left (t \right )+3 y \left (t \right )=3 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-6 y \left (t \right ) \\ y^{\prime }\left (t \right )=6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-14 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 y \left (t \right )-3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=3 y \left (t \right )-3 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-10 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=9 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right )+1 \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=2 x \left (t \right )-10 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+\cos \left (w t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right )+3 \\ y^{\prime }\left (t \right )=7 x \left (t \right )+5 y \left (t \right )+2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+7 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 x \left (t \right )-4 y \left (t \right )={\mathrm e}^{t} \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )={\mathrm e}^{4 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=-2 t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right )=t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right )={\mathrm e}^{t} \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )={\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right )=2 \,{\mathrm e}^{t} \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )={\mathrm e}^{-t} \\ x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right )=t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-4 x \left (t \right )-y \left (t \right )={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-6 y \left (t \right )={\mathrm e}^{3 t} \\ x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-6 y \left (t \right )=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right )=3 t \\ x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-3 y \left (t \right )=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right )=\sin \left (t \right ) \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right )=t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right )=4 t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right )=2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )+5 y \left (t \right )=t^{2} \\ x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right )=2 t +1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )=t^{2}+4 t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right )=2 t^{2}-2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right )=t -1 \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )=t +2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+4 y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right )=3 \,{\mathrm e}^{t} \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right )={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=-2 t \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right )=t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right )=1 \\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right )=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+2 y \left (t \right )+5 t \\ y^{\prime }\left (t \right )=3 x \left (t \right )+4 y \left (t \right )+17 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+7 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=7 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right )-4 z \left (t \right ) \\ z^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )-4 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=-3 x \left (t \right )-6 y \left (t \right )+6 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )+t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right )+\cos \left (2 t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{3 t} \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+\cos \left (3 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right )+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )+14 y \left (t \right ) \\ y^{\prime }\left (t \right )=7 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )+14 y \left (t \right ) \\ y^{\prime }\left (t \right )=7 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=-5 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=11 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+20 y \left (t \right ) \\ y^{\prime }\left (t \right )=40 x \left (t \right )-19 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-6 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-11 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=13 x \left (t \right )-9 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=10 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-6 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=13 x \left (t \right ) \\ y^{\prime }\left (t \right )=13 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )-4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right )={\mathrm e}^{t} \\ y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )^{2}}{x \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )}{2}-\frac {3 y \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right )=0 \\ y^{\prime }\left (t \right )+y \left (t \right )-x \left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+5 x \left (t \right )-2 y \left (t \right )=0 \\ y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right )=0 \\ y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+x \left (t \right )-z \left (t \right )=0 \\ x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right )=0 \\ z^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right )-3 z \left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {x \left (t \right )}{2}+2 y \left (t \right )-3 z \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right )-\frac {z \left (t \right )}{2} \\ z^{\prime }\left (t \right )=-2 x \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=y \left (t \right ) \\ x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )=t \\ x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-t \\ 2 x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right )=2 x \left (t \right )+6 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=t \\ 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 5 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ 3 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right )=0 \\ 2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right )=y \left (t \right )+t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )=\sin \left (t \right ) \\ x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+9 y \left (t \right )+12 \,{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=-5 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-7 x \left (t \right )+6 y \left (t \right )+6 \,{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )=-12 x \left (t \right )+5 y \left (t \right )+37 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-7 x \left (t \right )+10 y \left (t \right )+18 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=-10 x \left (t \right )+9 y \left (t \right )+37 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-14 x \left (t \right )+39 y \left (t \right )+78 \sinh \left (t \right ) \\ y^{\prime }\left (t \right )=-6 x \left (t \right )+16 y \left (t \right )+6 \cosh \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right )-2 \sinh \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+10 \cosh \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+6 y \left (t \right )-2 z \left (t \right )+50 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=6 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+21 \,{\mathrm e}^{-t} \\ z^{\prime }\left (t \right )=-x \left (t \right )+6 y \left (t \right )+z \left (t \right )+9 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ) \\ z^{\prime }\left (t \right )=-4 x \left (t \right )-2 y \left (t \right )+6 z \left (t \right )+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+2 z \left (t \right )+2 \,{\mathrm e}^{-t} \\ z^{\prime }\left (t \right )=-2 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )+y \left (t \right )-1-6 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+3 y \left (t \right )+4 \,{\mathrm e}^{t}-3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right )+24 \sin \left (t \right ) \\ y^{\prime }\left (t \right )=9 x \left (t \right )-3 y \left (t \right )+12 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=7 x \left (t \right )-4 y \left (t \right )+10 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=3 x \left (t \right )+14 y \left (t \right )+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-7 x \left (t \right )+4 y \left (t \right )+6 \,{\mathrm e}^{3 t} \\ y^{\prime }\left (t \right )=-5 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t} \\ z^{\prime }\left (t \right )=5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )-z \left (t \right )+5 \sin \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right )-10 \cos \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right )+2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \sin \left (2 t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-5 y \left (t \right )-3 z \left (t \right )+5 \cos \left (2 t \right ) \\ z^{\prime }\left (t \right )=-3 x \left (t \right )+7 y \left (t \right )+3 z \left (t \right )+23 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right )-3 z \left (t \right )+2 \,{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right )+2 z \left (t \right )+4 \,{\mathrm e}^{t} \\ z^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right )+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+5 y \left (t \right )+10 \sinh \left (t \right ) \\ y^{\prime }\left (t \right )=19 x \left (t \right )-13 y \left (t \right )+24 \sinh \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=9 x \left (t \right )-3 y \left (t \right )-6 t \\ y^{\prime }\left (t \right )=-x \left (t \right )+11 y \left (t \right )+10 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+1 \\ y^{\prime }\left (t \right )=x \left (t \right )+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right )=\sin \left (t \right ) \\ x^{\prime }\left (t \right )+y \left (t \right )=\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-10 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=12 x \left (t \right )+18 y \left (t \right ) \\ y^{\prime }\left (t \right )=-8 x \left (t \right )-12 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=0 \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-3 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )-2 y_{2} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )-2 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+3 y_{2} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )+2 y_{2} \left (x \right )+x -1 \\ y_{2}^{\prime }\left (x \right )=3 y_{1} \left (x \right )+2 y_{2} \left (x \right )-5 x -2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+1-6 x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=3 y_{1} \left (x \right )-2 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-y_{1} \left (x \right )+y_{2} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=\tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=\tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )={\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {x +1}\, y_{2} \left (x \right )+x^{2} \\ y_{2}^{\prime }\left (x \right )=\frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )={\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {x +1}\, y_{2} \left (x \right )+x^{2} \\ y_{2}^{\prime }\left (x \right )=\frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+5 \,{\mathrm e}^{x} \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 \,{\mathrm e}^{-x} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{2} \left (x \right )-2 y_{1} \left (x \right )+\sin \left (2 x \right ) \\ y_{2}^{\prime }\left (x \right )=-3 y_{1} \left (x \right )+y_{2} \left (x \right )-2 \cos \left (3 x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=3 y_{1} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=2 y_{3} \left (x \right )-y_{1} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 x y_{1} \left (x \right )-x^{2} y_{2} \left (x \right )+4 x \\ y_{2}^{\prime }\left (x \right )={\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-3 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )-2 y_{2} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+4 x -2 \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )-2 y_{2} \left (x \right )+3 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x} \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+y_{2} \left (x \right )-2 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=3 y_{2} \left (x \right )-2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=3 y_{1} \left (x \right )+y_{2} \left (x \right )-3 y_{3} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=5 y_{1} \left (x \right )-5 y_{2} \left (x \right )-5 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-y_{1} \left (x \right )+4 y_{2} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=3 y_{1} \left (x \right )-5 y_{2} \left (x \right )-3 y_{3} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=4 y_{1} \left (x \right )+6 y_{2} \left (x \right )+6 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+3 y_{2} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=-y_{1} \left (x \right )-4 y_{2} \left (x \right )-3 y_{3} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )+2 y_{2} \left (x \right )-3 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-3 y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+y_{3} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=-2 y_{1} \left (x \right )-y_{2} \left (x \right )+y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-y_{1} \left (x \right )-2 y_{2} \left (x \right )-y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=y_{1} \left (x \right )-y_{2} \left (x \right )-2 y_{3} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+2 y_{2} \left (x \right )+4 y_{3} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-y_{1} \left (x \right )+2 y_{2} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=3 y_{3} \left (x \right )-4 y_{4} \left (x \right ) \\ y_{4}^{\prime }\left (x \right )=4 y_{3} \left (x \right )+3 y_{4} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-3 y_{1} \left (x \right )+2 y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=y_{4} \left (x \right ) \\ y_{4}^{\prime }\left (x \right )=2 y_{1} \left (x \right )-5 y_{3} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=3 y_{1} \left (x \right )+2 y_{2} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=-2 y_{1} \left (x \right )+3 y_{2} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=y_{3} \left (x \right ) \\ y_{4}^{\prime }\left (x \right )=2 y_{4} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=y_{2} \left (x \right )+y_{4} \left (x \right ) \\ y_{2}^{\prime }\left (x \right )=y_{1} \left (x \right )-y_{3} \left (x \right ) \\ y_{3}^{\prime }\left (x \right )=y_{4} \left (x \right ) \\ y_{4}^{\prime }\left (x \right )=y_{3} \left (x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )-y \left (t \right )+2 \\ y^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right )-3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right )-6 \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right )+2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 \pi y \left (t \right )-\frac {x \left (t \right )}{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} p^{\prime }\left (t \right )=3 p \left (t \right )-2 q \left (t \right )-7 r \left (t \right ) \\ q^{\prime }\left (t \right )=-2 p \left (t \right )+6 r \left (t \right ) \\ r^{\prime }\left (t \right )=\frac {73 q \left (t \right )}{100}+2 r \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+2 \pi y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\beta y \left (t \right ) \\ y^{\prime }\left (t \right )=\gamma x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=1 \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {x \left (t \right )}{2} \\ y^{\prime }\left (t \right )=x \left (t \right )-\frac {y \left (t \right )}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=9 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-6 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-6 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-3 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {9 x \left (t \right )}{10}-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+\frac {11 y \left (t \right )}{10} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+10 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {y \left (t \right )}{10} \\ y^{\prime }\left (t \right )=\frac {z \left (t \right )}{5} \\ z^{\prime }\left (t \right )=\frac {2 x \left (t \right )}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \\ z^{\prime }\left (t \right )=2 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+3 z \left (t \right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \\ z^{\prime }\left (t \right )=-3 x \left (t \right )+z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=2 y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )=-y \left (t \right )+2 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-4 y \left (t \right ) \\ z^{\prime }\left (t \right )=-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-4 y \left (t \right ) \\ z^{\prime }\left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=-2 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right ) \\ z^{\prime }\left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right )+3 z \left (t \right ) \\ z^{\prime }\left (t \right )=-x \left (t \right )+3 y \left (t \right )-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )+3 y \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=5 x \left (t \right )-5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-10 x \left (t \right )+10 y \left (t \right ) \\ y^{\prime }\left (t \right )=28 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )=-\frac {8 z \left (t \right )}{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=z \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right )-x \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right ) \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=0 \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\pi ^{2} x \left (t \right )+\frac {187 y \left (t \right )}{5} \\ y^{\prime }\left (t \right )=\sqrt {555}\, x \left (t \right )+\frac {400617 y \left (t \right )}{5000} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right )-4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=1-2 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-3 y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )-7 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )=15 y \left (t \right ) \\ t y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=5 x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-13 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )+2 y \left (t \right )-17 \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )-13 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )+2 y \left (t \right )+7 \,{\mathrm e}^{2 t} \\ y^{\prime }\left (t \right )=4 x \left (t \right )+y \left (t \right )-7 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+3 y \left (t \right )-6 \,{\mathrm e}^{3 t} \\ y^{\prime }\left (t \right )=x \left (t \right )+6 y \left (t \right )+2 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+24 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-13 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+3 y \left (t \right )+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+6 y \left (t \right )+17 \operatorname {Heaviside}\left (t -2\right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=8 x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=3 x \left (t \right )-7 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-5 y \left (t \right )+4 \\ y^{\prime }\left (t \right )=3 x \left (t \right )-7 y \left (t \right )+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=6 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) y \left (t \right )-6 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )-5 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 y \left (t \right ) \\ y^{\prime }\left (t \right )=-4 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 \\ y^{\prime }\left (t \right )=\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \\ y^{\prime }\left (t \right )=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=0 \\ y^{\prime }\left (t \right )=-2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )^{2} \\ y^{\prime }\left (t \right )={\mathrm e}^{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-3 x_{1} \left (t \right ) \\ x_{2}^{\prime }\left (t \right )=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-x_{1} \left (t \right )+1 \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-3 x \left (t \right )+6 y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )-y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+6 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )+2 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+\sin \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 t x_{1} \left (t \right )^{2} \\ x_{2}^{\prime }\left (t \right )=\frac {x_{2} \left (t \right )+t}{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )={\mathrm e}^{t -x_{1} \left (t \right )} \\ x_{2}^{\prime }\left (t \right )=2 \,{\mathrm e}^{x_{1} \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )^{2}}{x \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=\frac {x_{1} \left (t \right )^{2}}{x_{2} \left (t \right )} \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right )-x_{1} \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {{\mathrm e}^{-x \left (t \right )}}{t} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right ) {\mathrm e}^{-y \left (t \right )}}{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )-t}{x \left (t \right )+y \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {t -y \left (t \right )}{-x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )-t}{-x \left (t \right )+y \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-9 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+t \\ y^{\prime }\left (t \right )=x \left (t \right )-t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right )=0 \\ y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right )=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+5 y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right )=\sin \left (t \right ) \\ x^{\prime }\left (t \right )+y \left (t \right )=\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=z \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=z \left (t \right ) \\ z^{\prime }\left (t \right )=z \left (t \right )-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=y \left (t \right ) \\ y^{\prime \prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )=0 \\ x^{\prime }\left (t \right )+y^{\prime \prime }\left (t \right )=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right )^{2} \\ y^{\prime }\left (t \right )=2 x \left (t \right ) y \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {1}{y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {1}{x \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {x \left (t \right )}{y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )}{x \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {y \left (t \right )}{x \left (t \right )-y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )}{x \left (t \right )-y \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\sin \left (x \left (t \right )\right ) \cos \left (y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=\cos \left (x \left (t \right )\right ) \sin \left (y \left (t \right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} {\mathrm e}^{t} x^{\prime }\left (t \right )=\frac {1}{y \left (t \right )} \\ {\mathrm e}^{t} y^{\prime }\left (t \right )=\frac {1}{x \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=\cos \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}+\sin \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2} \\ y^{\prime }\left (t \right )=-\frac {\sin \left (2 x \left (t \right )\right ) \sin \left (2 y \left (t \right )\right )}{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=8 y \left (t \right )-x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right )+4 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-5 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+z \left (t \right )-x \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right )-z \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+2 z \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-y \left (t \right )+z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+z \left (t \right ) \\ z^{\prime }\left (t \right )=y \left (t \right )-2 z \left (t \right )-3 x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right )=-{\mathrm e}^{2 t} \\ y^{\prime }\left (t \right )+3 x \left (t \right )-2 y \left (t \right )=6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-\cos \left (t \right ) \\ y^{\prime }\left (t \right )=-y \left (t \right )-2 x \left (t \right )+\cos \left (t \right )+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )+\tan \left (t \right )^{2}-1 \\ y^{\prime }\left (t \right )=\tan \left (t \right )-x \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-2 y \left (t \right )+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }\left (t \right )=6 x \left (t \right )+3 y \left (t \right )-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+\frac {1}{\cos \left (t \right )} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3-2 y \left (t \right ) \\ y^{\prime }\left (t \right )=2 x \left (t \right )-2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=-y \left (t \right )+\sin \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=4 x \left (t \right )-5 y \left (t \right )+4 t -1 \\ y^{\prime }\left (t \right )=x \left (t \right )-2 y \left (t \right )+t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )-x \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y \left (t \right )=t^{2} \\ y^{\prime }\left (t \right )-x \left (t \right )=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )={\mathrm e}^{-t} \\ 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right )=\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+y \left (t \right )-2 z \left (t \right )+2-t \\ y^{\prime }\left (t \right )=-x \left (t \right )+1 \\ z^{\prime }\left (t \right )=x \left (t \right )+y \left (t \right )-z \left (t \right )+1-t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right )=2 \,{\mathrm e}^{-t} \\ y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right )=1 \\ z^{\prime }\left (t \right )+z \left (t \right )=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=5 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )+2 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=6 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=4 x \left (t \right )+3 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )-4 y \left (t \right )+1 \\ y^{\prime }\left (t \right )=-x \left (t \right )+5 y \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{t} \\ y^{\prime }\left (t \right )=x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }\left (t \right )=2 x \left (t \right )+4 y \left (t \right )+\cos \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right )-2 y \left (t \right )+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|