|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{t} \\ y^{\prime }=x-y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.656 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.509 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=-2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.520 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.517 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+5 y+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.958 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y+{\mathrm e}^{t} \\ y^{\prime }=x-y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.572 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y+\sin \left (t \right ) \\ y^{\prime }=x-2 y+\tan \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.706 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\textit {f\_1} \left (t \right ) \\ y^{\prime }=-x+f_{2} \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.059 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }-8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.724 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \tan \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.531 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = g \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.661 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = g \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.017 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 2 t^{2}+4 \sin \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.917 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = t +\cos \left (t \right )+2 \,{\mathrm e}^{-2 t}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.211 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = t +\sin \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.894 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = t^{2} \sin \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.194 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = t^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.157 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = t +{\mathrm e}^{-t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = t^{3} {\mathrm e}^{-t}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.165 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1}-3 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=-4 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.343 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.453 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.504 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+6 x_{3} \\ x_{2}^{\prime }=5 x_{2} \\ x_{3}^{\prime }=6 x_{1}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.368 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+3 x_{3}+6 x_{4} \\ x_{2}^{\prime }=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4} \\ x_{3}^{\prime }=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4} \\ x_{4}^{\prime }=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.560 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=4 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.458 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }=3 x_{1}+3 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.387 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+10 x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.508 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}-2 x_{3} \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.495 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \\ x_{3}^{\prime }=x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.521 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=3 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.583 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{3} \\ x_{2}^{\prime }=x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{1}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.564 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.539 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.209 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1} \\ x_{3}^{\prime }=-3 x_{4} \\ x_{4}^{\prime }=3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.128 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.334 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.441 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.315 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{3} \\ x_{2}^{\prime }=2 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3} \\ x_{4}^{\prime }=-x_{3}+2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.383 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }=-x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.374 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-4 x_{2} \\ x_{2}^{\prime }=10 x_{1}+9 x_{2}+x_{3} \\ x_{3}^{\prime }=-4 x_{1}-3 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.491 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.400 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=2 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.357 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.261 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+{\mathrm e}^{c t} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.317 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.948 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.584 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\tan \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.774 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+f_{2} \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.067 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=x_{2}+3 x_{3}+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.564 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}-2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.704 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+{\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.746 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-t^{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.508 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2}+2 x_{3}+\sin \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.110 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3}-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.700 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }=-4 x_{2}-x_{3}+t \\ x_{3}^{\prime }=5 x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.273 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.961 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+x_{3}-{\mathrm e}^{3 t} \\ x_{3}^{\prime }=-3 x_{1}+x_{2}-x_{3}-{\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.805 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.727 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.373 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.441 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2}+t \\ x_{2}^{\prime }=2 x_{1}-2 x_{2}+3 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.317 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}+x_{2}-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.311 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.289 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\tan \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
32.380 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.377 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+f_{2} \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.852 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.504 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.463 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.234 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=3 x_{3}+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.215 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.561 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.267 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=2 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.239 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2}-2 x y \\ y^{\prime }=2 y-2 y^{2}-3 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-b x y+m \\ y^{\prime }=b x y-g y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x-b x y \\ y^{\prime }=-c y+d x y \\ z^{\prime }=z+x^{2}+y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-x \,y^{2} \\ y^{\prime }=-y-y \,x^{2} \\ z^{\prime }=1-z+x^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \,y^{2}-x \\ y^{\prime }=x \sin \left (\pi y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\cos \left (y\right ) \\ y^{\prime }=\sin \left (x\right )-1 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.025 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-1-y-{\mathrm e}^{x} \\ y^{\prime }=x^{2}+y \left ({\mathrm e}^{x}-1\right ) \\ z^{\prime }=x+\sin \left (z\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y^{2} \\ y^{\prime }=x^{2}-y \\ z^{\prime }={\mathrm e}^{z}-x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+z-2 \,{\mathrm e}^{-t} \\ y^{\prime }=2 x+y-z-2 \,{\mathrm e}^{-t} \\ z^{\prime }=-3 x+2 y+4 z+3 \,{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.700 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.315 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|