|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.069 |
|
|
\[
{}t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y = \ln \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.064 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.068 |
|
|
\[
{}\left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.065 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.342 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.155 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.123 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}-4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+4 x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.335 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-4 x_{1}+2 x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-2 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=-2 x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+4 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+6 x_{3} \\ x_{2}^{\prime }=x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=6 x_{1}+x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.520 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }=2 x_{2}+2 x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.448 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{3} \\ x_{2}^{\prime }=2 x_{1} \\ x_{3}^{\prime }=-x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.487 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{3} \\ x_{2}^{\prime }=-2 x_{2} \\ x_{3}^{\prime }=3 x_{1}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.589 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2} \\ x_{2}^{\prime }=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2} \\ x_{3}^{\prime }=-2 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.494 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+5 x_{2}+3 x_{3}-5 x_{4} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4} \\ x_{3}^{\prime }=-x_{2}-2 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.706 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}+x_{2}-4 x_{3}-x_{4} \\ x_{2}^{\prime }=-3 x_{2} \\ x_{3}^{\prime }=x_{1}-x_{2}+x_{4} \\ x_{4}^{\prime }=2 x_{1}-x_{2}+2 x_{3}-2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.661 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+2 x_{2}-x_{4} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+2 x_{4} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=-x_{1}+2 x_{2}+2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.483 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+8 x_{2}+5 x_{3}+3 x_{4} \\ x_{2}^{\prime }=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4} \\ x_{3}^{\prime }=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4} \\ x_{4}^{\prime }=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.831 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}-2 x_{4} \\ x_{2}^{\prime }=-x_{1}+3 x_{2}-x_{3}+x_{4} \\ x_{3}^{\prime }=-2 x_{1}-2 x_{2}-4 x_{3}+2 x_{4} \\ x_{4}^{\prime }=-7 x_{1}+x_{2}-7 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.750 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\ x_{2}^{\prime }=-3 x_{2} \\ x_{3}^{\prime }=x_{1}-x_{3}-x_{5} \\ x_{4}^{\prime }=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\ x_{5}^{\prime }=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.978 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\ x_{2}^{\prime }=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\ x_{3}^{\prime }=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\ x_{4}^{\prime }=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\ x_{5}^{\prime }=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.512 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-3 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+3 x_{3} \\ x_{3}^{\prime }=3 x_{1}-4 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.663 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-2 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.586 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=-6 x_{1}-3 x_{3} \\ x_{3}^{\prime }=\frac {8 x_{2}}{3}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.652 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }=-x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.635 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }=3 x_{1}-2 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.649 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.523 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\ x_{3}^{\prime }=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.645 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\ x_{2}^{\prime }=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\ x_{3}^{\prime }=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\ x_{4}^{\prime }=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.976 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4} \\ x_{3}^{\prime }=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4} \\ x_{4}^{\prime }=2 x_{1}-2 x_{2}-6 x_{3}+x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.092 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\ x_{2}^{\prime }=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\ x_{3}^{\prime }=-2 x_{1}-x_{3}+2 x_{4} \\ x_{4}^{\prime }=-2 x_{2}+2 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.438 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\ x_{2}^{\prime }=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\ x_{3}^{\prime }=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\ x_{4}^{\prime }=-2 x_{2}+2 x_{3}+4 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.391 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{2}-2 x_{4} \\ x_{2}^{\prime }=-\frac {x_{1}}{2}+x_{2}-3 x_{3}-\frac {5 x_{4}}{2} \\ x_{3}^{\prime }=3 x_{2}-5 x_{3}-3 x_{4} \\ x_{4}^{\prime }=x_{1}+3 x_{2}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.108 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=\frac {x_{1}}{2}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\ x_{2}^{\prime }=x_{1}-\frac {x_{2}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.356 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {x_{1}}{2}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.414 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.494 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}+\frac {x_{2}}{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.698 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {5 x_{1}}{2}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.396 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.522 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.531 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.518 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.306 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.310 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.310 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.208 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-k_{1} x_{1} \\ x_{2}^{\prime }=k_{1} x_{1}-k_{2} x_{2} \\ x_{3}^{\prime }=k_{2} x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.495 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.803 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.523 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=1-x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{2}+t \\ x_{3}^{\prime }=-2 x_{1}-x_{2}+3 x_{3}+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.592 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\ x_{2}^{\prime }=-x_{1}-2 x_{2}+x_{3}+t \\ x_{3}^{\prime }=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.734 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+x_{2}+3 x_{3}+3 t \\ x_{2}^{\prime }=-2 x_{2} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.786 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}+x_{2}+\frac {x_{3}}{2} \\ x_{2}^{\prime }=x_{1}-x_{2}+x_{3}-\sin \left (t \right ) \\ x_{3}^{\prime }=\frac {x_{1}}{2}+x_{2}-\frac {x_{3}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.867 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+1 \\ x_{2}^{\prime }=x_{1}-2 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
311.664 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.389 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.358 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-3 x_{2}-2 x_{3} \\ x_{2}^{\prime }=8 x_{1}-5 x_{2}-4 x_{3} \\ x_{3}^{\prime }=-4 x_{1}+3 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.442 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+9 x_{2}-6 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+11 x_{2}-7 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+3 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+6 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.435 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\ x_{2}^{\prime }=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\ x_{3}^{\prime }=-2 x_{1}-2 x_{3}-3 x_{4} \\ x_{4}^{\prime }=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.243 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\ x_{2}^{\prime }=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\ x_{3}^{\prime }=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\ x_{4}^{\prime }=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.601 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.521 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=6 x_{1}+4 x_{2}+6 x_{3} \\ x_{3}^{\prime }=-5 x_{1}-2 x_{2}-4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.483 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=-14 x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }=15 x_{1}+5 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.482 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y+x y \\ y^{\prime }=x+4 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=1+5 y \\ y^{\prime }=1-6 x^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}y^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.726 |
|
|
\[
{}y^{\prime } = -x^{3}
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}y^{\prime \prime } = \sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.039 |
|
|
\[
{}x \sqrt {1+y^{2}}+y \sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
6.117 |
|
|
\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
36.569 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }+\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
16.749 |
|
|
\[
{}y^{\prime } = \frac {2 x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.112 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.188 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.187 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.549 |
|