|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{5}+y = k \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.295 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{10}+y = k \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.219 |
|
|
\[
{}y^{\prime \prime }+w^{2} y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.523 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = \sin \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.451 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+17 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.709 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.862 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.438 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.388 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = g \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.813 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = g \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
5.960 |
|
|
\[
{}\frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.330 |
|
|
\[
{}\frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.338 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.474 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.545 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y = t
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.129 |
|
|
\[
{}t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.050 |
|
|
\[
{}t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.047 |
|
|
\[
{}y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y = \ln \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.041 |
|
|
\[
{}\left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}\left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.041 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.107 |
|
|
\[
{}t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.049 |
|
|
\[
{}t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.048 |
|
|
\[
{}y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y = \ln \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.042 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}\left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.044 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.380 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.047 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.051 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.054 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.149 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.107 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}-4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.434 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+4 x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.381 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-4 x_{1}+2 x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-2 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.446 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=-2 x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+4 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+6 x_{3} \\ x_{2}^{\prime }=x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=6 x_{1}+x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.484 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.420 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.550 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.536 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }=2 x_{2}+2 x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.442 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{3} \\ x_{2}^{\prime }=2 x_{1} \\ x_{3}^{\prime }=-x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.484 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{3} \\ x_{2}^{\prime }=-2 x_{2} \\ x_{3}^{\prime }=3 x_{1}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.686 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2} \\ x_{2}^{\prime }=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2} \\ x_{3}^{\prime }=-2 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.492 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+5 x_{2}+3 x_{3}-5 x_{4} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4} \\ x_{3}^{\prime }=-x_{2}-2 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.741 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}+x_{2}-4 x_{3}-x_{4} \\ x_{2}^{\prime }=-3 x_{2} \\ x_{3}^{\prime }=x_{1}-x_{2}+x_{4} \\ x_{4}^{\prime }=2 x_{1}-x_{2}+2 x_{3}-2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.705 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+2 x_{2}-x_{4} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+2 x_{4} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=-x_{1}+2 x_{2}+2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+8 x_{2}+5 x_{3}+3 x_{4} \\ x_{2}^{\prime }=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4} \\ x_{3}^{\prime }=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4} \\ x_{4}^{\prime }=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.871 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}-2 x_{4} \\ x_{2}^{\prime }=-x_{1}+3 x_{2}-x_{3}+x_{4} \\ x_{3}^{\prime }=-2 x_{1}-2 x_{2}-4 x_{3}+2 x_{4} \\ x_{4}^{\prime }=-7 x_{1}+x_{2}-7 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.832 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\ x_{2}^{\prime }=-3 x_{2} \\ x_{3}^{\prime }=x_{1}-x_{3}-x_{5} \\ x_{4}^{\prime }=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\ x_{5}^{\prime }=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.114 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\ x_{2}^{\prime }=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\ x_{3}^{\prime }=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\ x_{4}^{\prime }=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\ x_{5}^{\prime }=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.829 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-3 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.707 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+3 x_{3} \\ x_{3}^{\prime }=3 x_{1}-4 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.710 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-2 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.683 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=-6 x_{1}-3 x_{3} \\ x_{3}^{\prime }=\frac {8 x_{2}}{3}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.734 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }=-x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.726 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }=3 x_{1}-2 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.748 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.607 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.527 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\ x_{3}^{\prime }=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.743 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\ x_{2}^{\prime }=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\ x_{3}^{\prime }=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\ x_{4}^{\prime }=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
4.418 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4} \\ x_{3}^{\prime }=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4} \\ x_{4}^{\prime }=2 x_{1}-2 x_{2}-6 x_{3}+x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.178 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\ x_{2}^{\prime }=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\ x_{3}^{\prime }=-2 x_{1}-x_{3}+2 x_{4} \\ x_{4}^{\prime }=-2 x_{2}+2 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.847 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\ x_{2}^{\prime }=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\ x_{3}^{\prime }=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\ x_{4}^{\prime }=-2 x_{2}+2 x_{3}+4 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.868 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{2}-2 x_{4} \\ x_{2}^{\prime }=-\frac {x_{1}}{2}+x_{2}-3 x_{3}-\frac {5 x_{4}}{2} \\ x_{3}^{\prime }=3 x_{2}-5 x_{3}-3 x_{4} \\ x_{4}^{\prime }=x_{1}+3 x_{2}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.179 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=\frac {x_{1}}{2}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.466 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.443 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\ x_{2}^{\prime }=x_{1}-\frac {x_{2}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.407 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {x_{1}}{2}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.527 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}+\frac {x_{2}}{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.494 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.782 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {5 x_{1}}{2}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.450 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.552 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.531 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.584 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.565 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.300 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.289 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.300 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.198 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-k_{1} x_{1} \\ x_{2}^{\prime }=k_{1} x_{1}-k_{2} x_{2} \\ x_{3}^{\prime }=k_{2} x_{2} \end {array}\right ]
\] |
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 |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.688 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.880 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.544 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=1-x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{2}+t \\ x_{3}^{\prime }=-2 x_{1}-x_{2}+3 x_{3}+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.685 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\ x_{2}^{\prime }=-x_{1}-2 x_{2}+x_{3}+t \\ x_{3}^{\prime }=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.756 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+x_{2}+3 x_{3}+3 t \\ x_{2}^{\prime }=-2 x_{2} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.817 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}+x_{2}+\frac {x_{3}}{2} \\ x_{2}^{\prime }=x_{1}-x_{2}+x_{3}-\sin \left (t \right ) \\ x_{3}^{\prime }=\frac {x_{1}}{2}+x_{2}-\frac {x_{3}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.921 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+1 \\ x_{2}^{\prime }=x_{1}-2 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
291.682 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.442 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.419 |
|