|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = -12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.231 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y = -{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.405 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (x +1\right )+{\mathrm e}^{-2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.202 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = \sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.192 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y = {\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.207 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y = {\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.902 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = {\mathrm e}^{2 x} \left (10+3 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = -{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.153 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = -2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (x +1\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.144 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = -{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.163 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.228 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.328 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y = {\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.730 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x} \left (1-6 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.210 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{-x} \left (-8 x +4\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.227 |
|
|
\[
{}4 y^{\prime \prime \prime }-3 y^{\prime }-y = {\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.258 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \left (20-12 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.176 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y = 30 \cos \left (x \right )-10 \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.609 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime } = -2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right )
\] |
[[_high_order, _missing_y]] |
✓ |
1.814 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 2 x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.257 |
|
|
\[
{}4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y = 30 x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.310 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.264 |
|
|
\[
{}16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y = 96 x^{{5}/{2}}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.360 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y = x^{4}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.320 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 12 x^{2}
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.334 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 4 x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.385 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.385 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y = 9 x^{4}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.399 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \left (x +1\right )
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.290 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 9 x^{2}
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.437 |
|
|
\[
{}4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y = 6 x
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.467 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y = 40 x^{3}
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = F \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.549 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = F \left (x \right )
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.545 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = F \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.546 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = F \left (x \right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.625 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2} \\ y_{2}^{\prime }=2 y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.325 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4} \\ y_{2}^{\prime }=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.331 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\ y_{2}^{\prime }=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.352 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-4 y_{2} \\ y_{2}^{\prime }=-y_{1}-y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-4 y_{2} \\ y_{2}^{\prime }=-y_{1}-y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-3 y_{2} \\ y_{2}^{\prime }=2 y_{1}-y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.341 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.340 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{2}^{\prime }=y_{1}-2 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-4 y_{1}+y_{2}-y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.551 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-4 y_{2}-8 y_{3} \\ y_{2}^{\prime }=-4 y_{1}-4 y_{3} \\ y_{3}^{\prime }=-8 y_{1}-4 y_{2}-6 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.485 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+5 y_{2}+8 y_{3} \\ y_{2}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }=-y_{1}-y_{2}-y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.549 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2}+2 y_{3} \\ y_{2}^{\prime }=12 y_{1}-4 y_{2}+10 y_{3} \\ y_{3}^{\prime }=-6 y_{1}+y_{2}-7 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-y_{2}-4 y_{3} \\ y_{2}^{\prime }=4 y_{1}-3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+2 y_{2}-6 y_{3} \\ y_{2}^{\prime }=2 y_{1}+6 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-2 y_{1}-2 y_{2}+2 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.518 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-2 y_{1}+7 y_{2}-2 y_{3} \\ y_{3}^{\prime }=-10 y_{1}+10 y_{2}-5 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=3 y_{1}+5 y_{2}+y_{3} \\ y_{3}^{\prime }=-6 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-y_{1}+7 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.319 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.303 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-y_{1}-11 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.315 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.297 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+12 y_{2} \\ y_{2}^{\prime }=-3 y_{1}-8 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.336 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }=-4 y_{1}+2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.332 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-13 y_{1}+16 y_{2} \\ y_{2}^{\prime }=-9 y_{1}+11 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2}+y_{3} \\ y_{2}^{\prime }=-4 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }=4 y_{2}+2 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\ y_{2}^{\prime }=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\ y_{3}^{\prime }=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=-2 y_{1}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}+3 y_{2}-y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-2 y_{1}+3 y_{2}-y_{3} \\ y_{3}^{\prime }=2 y_{1}-y_{2}+3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.477 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=6 y_{1}-5 y_{2}+3 y_{3} \\ y_{2}^{\prime }=2 y_{1}-y_{2}+3 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{2}+y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.478 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-11 y_{1}+8 y_{2} \\ y_{2}^{\prime }=-2 y_{1}-3 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.445 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=15 y_{1}-9 y_{2} \\ y_{2}^{\prime }=16 y_{1}-9 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.522 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-4 y_{2} \\ y_{2}^{\prime }=y_{1}-7 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.455 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+24 y_{2} \\ y_{2}^{\prime }=-6 y_{1}+17 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.468 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+3 y_{2} \\ y_{2}^{\prime }=-3 y_{1}-y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }=-y_{1}-y_{2}-y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.543 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+2 y_{2}+y_{3} \\ y_{2}^{\prime }=-2 y_{1}+2 y_{2}+y_{3} \\ y_{3}^{\prime }=-3 y_{1}+3 y_{2}+2 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}-4 y_{2}+4 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{3} \\ y_{3}^{\prime }=-9 y_{1}-5 y_{2}+6 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.800 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-4 y_{2}-y_{3} \\ y_{2}^{\prime }=3 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }=-3 y_{1}-2 y_{2}+3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.523 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-8 y_{2}-4 y_{3} \\ y_{2}^{\prime }=-3 y_{1}-y_{2}-4 y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}+9 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.575 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-5 y_{1}-y_{2}+11 y_{3} \\ y_{2}^{\prime }=-7 y_{1}+y_{2}+13 y_{3} \\ y_{3}^{\prime }=-4 y_{1}+8 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}+9 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+10 y_{2}-12 y_{3} \\ y_{2}^{\prime }=2 y_{1}+2 y_{2}+3 y_{3} \\ y_{3}^{\prime }=2 y_{1}-y_{2}+6 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-4 y_{2}-4 y_{3} \\ y_{2}^{\prime }=2 y_{1}-y_{2}+y_{3} \\ y_{3}^{\prime }=2 y_{1}+3 y_{2}+y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.446 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-y_{1}+5 y_{2}-3 y_{3} \\ y_{3}^{\prime }=y_{1}+y_{2}+y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.467 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-12 y_{2}+10 y_{3} \\ y_{2}^{\prime }=2 y_{1}-24 y_{2}+11 y_{3} \\ y_{3}^{\prime }=2 y_{1}-24 y_{2}+8 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.502 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-12 y_{2}+8 y_{3} \\ y_{2}^{\prime }=y_{1}-9 y_{2}+4 y_{3} \\ y_{3}^{\prime }=y_{1}-6 y_{2}+y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{3} \\ y_{2}^{\prime }=-y_{1}-3 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-2 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.391 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-3 y_{2}+4 y_{3} \\ y_{2}^{\prime }=4 y_{1}+5 y_{2}-8 y_{3} \\ y_{3}^{\prime }=2 y_{1}+3 y_{2}-5 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2} \\ y_{3}^{\prime }=-y_{1}-y_{2}-2 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.364 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+2 y_{2} \\ y_{2}^{\prime }=-5 y_{1}+5 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.458 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-26 y_{1}+9 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.447 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2} \\ y_{2}^{\prime }=-4 y_{1}+5 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-6 y_{2} \\ y_{2}^{\prime }=3 y_{1}-y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-3 y_{2}+y_{3} \\ y_{2}^{\prime }=2 y_{2}+2 y_{3} \\ y_{3}^{\prime }=5 y_{1}+y_{2}+y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
8.519 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}+3 y_{2}+y_{3} \\ y_{2}^{\prime }=y_{1}-5 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-3 y_{1}+7 y_{2}+3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.723 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=y_{2}+y_{3} \\ y_{3}^{\prime }=y_{1}+y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}+y_{2}-3 y_{3} \\ y_{2}^{\prime }=4 y_{1}-y_{2}+2 y_{3} \\ y_{3}^{\prime }=4 y_{1}-2 y_{2}+3 y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.773 |
|
|
\[
{}y^{\prime }+\sin \left (t \right ) y = 0
\] |
[_separable] |
✓ |
0.345 |
|
|
\[
{}y^{\prime }+{\mathrm e}^{t^{2}} y = 0
\] |
[_separable] |
✓ |
0.370 |
|
|
\[
{}y^{\prime }-2 t y = t
\] |
[_separable] |
✓ |
0.189 |
|
|
\[
{}y^{\prime }+2 t y = t
\] |
[_separable] |
✓ |
0.322 |
|
|
\[
{}y^{\prime }+y = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
0.455 |
|
|
\[
{}\cos \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.425 |
|
|
\[
{}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.339 |
|