|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.143 |
|
|
\[
{}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.288 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.415 |
|
|
\[
{}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.361 |
|
|
\[
{}y^{\prime \prime }+x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.128 |
|
|
\[
{}y^{\prime \prime }+4 y = \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.447 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.380 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.226 |
|
|
\[
{}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.672 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-3 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.426 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-4 x_{1}-6 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.466 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=x_{2}-x_{3} \\ x_{3}^{\prime }=x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=-x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.589 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.521 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.509 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.478 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+t \\ x_{2}^{\prime }=-2 x_{1}+x_{2}+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2} \\ x_{2}^{\prime }=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.069 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.423 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-b x_{1}-a x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.604 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{2} \\ x_{2}^{\prime }=-3 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.446 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.538 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.463 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.382 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{t} \\ x_{2}^{\prime }=x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{t}+t x_{2} \\ x_{2}^{\prime }=-\frac {x_{1}}{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.062 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.429 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-7 x_{2} \\ x_{2}^{\prime }=-x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{2} \\ x_{2}^{\prime }=4 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=5 x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=5 x_{2}-7 x_{3} \\ x_{3}^{\prime }=2 x_{2}-4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.496 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1} \\ x_{2}^{\prime }=x_{1}+5 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+6 x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.378 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-x_{1} \\ x_{3}^{\prime }=5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.496 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+3 x_{3} \\ x_{2}^{\prime }=-4 x_{2} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+6 x_{3} \\ x_{2}^{\prime }=-2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=-x_{1}-2 x_{2}-4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{2}+x_{3} \\ x_{2}^{\prime }=-2 x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.448 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{3} \\ x_{2}^{\prime }=-3 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.612 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.429 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\ x_{3}^{\prime }=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\ x_{4}^{\prime }=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.745 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-x_{1} \\ x_{3}^{\prime }=-x_{4} \\ x_{4}^{\prime }=x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+4 x_{2} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.565 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-6 x_{2} \\ x_{2}^{\prime }=3 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.625 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.487 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{2} \\ x_{2}^{\prime }=-4 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.521 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-b x_{1}-a x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.608 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.397 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.399 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+3 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.442 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1} \\ x_{2}^{\prime }=x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.342 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=15 x_{1}-32 x_{2}+12 x_{3} \\ x_{2}^{\prime }=8 x_{1}-17 x_{2}+6 x_{3} \\ x_{3}^{\prime }=-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \\ x_{3}^{\prime }=x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.298 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-2 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.342 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+5 x_{2} \\ x_{3}^{\prime }=4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.328 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}-x_{1} \\ x_{2}^{\prime }=-2 x_{1}-3 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.426 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{1}+2 x_{3}+x_{4} \\ x_{4}^{\prime }=x_{2}+2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.864 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \\ x_{3}^{\prime }=x_{1}+x_{3}+x_{4} \\ x_{4}^{\prime }=x_{2}+x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.618 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{1}-x_{4} \\ x_{4}^{\prime }=x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.561 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-x_{1}-3 x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.371 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.526 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.484 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}+t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{2}+{\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.358 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+20 \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{1}+x_{2}+12 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.536 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2}+54 t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=-2 x_{1}+4 x_{2}+9 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.525 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+4 x_{2}+8 \sin \left (2 t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}+8 \cos \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.044 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=-2 x_{1}-x_{2}+6 t \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.497 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-{\mathrm e}^{t} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.650 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-2 x_{2}+2 x_{3}-{\mathrm e}^{3 t} \\ x_{2}^{\prime }=2 x_{1}+4 x_{2}-x_{3}+4 \,{\mathrm e}^{3 t} \\ x_{3}^{\prime }=3 x_{3}+3 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.605 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-3 x_{2}+34 \sin \left (t \right ) \\ x_{2}^{\prime }=-4 x_{1}-2 x_{2}+17 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.606 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.365 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.376 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=3 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.334 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.400 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=x_{2}-8 x_{3} \\ x_{3}^{\prime }=2 x_{2}-7 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.371 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
9.589 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}+6 x_{2}-3 x_{3} \\ x_{2}^{\prime }=-12 x_{1}+10 x_{2}-3 x_{3} \\ x_{3}^{\prime }=-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.434 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=6 x_{2}-7 x_{3}+3 x_{4} \\ x_{3}^{\prime }=3 x_{3}-x_{4} \\ x_{4}^{\prime }=-4 x_{2}+9 x_{3}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.606 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{2}-x_{4} \\ x_{4}^{\prime }=x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\left (2 t -1\right ) x_{1} \\ x_{2}^{\prime }={\mathrm e}^{-t^{2}+t} x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.063 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2} \\ x_{2}^{\prime }=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right ) \\ x_{3}^{\prime }=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-t \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.081 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{1}+x_{2} \\ x_{2}^{\prime }=6 x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}-2 x_{2} \\ x_{2}^{\prime }=5 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.435 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-5 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.394 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+4 x_{3} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=-4 x_{1}-5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.359 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.488 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+13 x_{2} \\ x_{2}^{\prime }=-x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.550 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-10 x_{2} \\ x_{2}^{\prime }=5 x_{1}+11 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.511 |
|