|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2}+x_{3} \\ x_{2}^{\prime }=4 x_{1}-9 x_{2}-x_{3} \\ x_{3}^{\prime }=3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.694 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1} \\ x_{2}^{\prime }=2 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }=5 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.707 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-4 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.599 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+3 x_{3} \\ x_{2}^{\prime }=-9 x_{1}-3 x_{2}-9 x_{3} \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.535 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-17 x_{1}-42 x_{3} \\ x_{2}^{\prime }=-7 x_{1}+4 x_{2}-14 x_{3} \\ x_{3}^{\prime }=7 x_{1}+18 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-16 x_{1}+30 x_{2}-18 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+8 x_{2}+16 x_{3} \\ x_{3}^{\prime }=8 x_{1}-15 x_{2}+9 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.490 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}-6 x_{2}-7 x_{3} \\ x_{2}^{\prime }=-3 x_{1}-3 x_{2}-3 x_{3} \\ x_{3}^{\prime }=7 x_{1}+6 x_{2}+7 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.417 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2}-2 x_{3} \\ x_{2}^{\prime }=x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+6 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2}-2 x_{3} \\ x_{2}^{\prime }=-4 x_{1}-5 x_{2}-6 x_{3} \\ x_{3}^{\prime }=4 x_{1}+8 x_{2}+7 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.751 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=4 x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.420 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-x_{2}-2 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.401 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.358 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+13 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \\ x_{3}^{\prime }=2 x_{3}+4 x_{4} \\ x_{4}^{\prime }=2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.740 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-x_{4} \\ x_{2}^{\prime }=6 x_{2} \\ x_{3}^{\prime }=-x_{3} \\ x_{4}^{\prime }=2 x_{1}+5 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.723 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{1}+x_{2}+1 \\ x_{2}^{\prime }=6 x_{1}-5 x_{2}+{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.607 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}-2 x_{2}+9 t \\ x_{2}^{\prime }=5 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.582 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.479 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t} \\ x_{2}^{\prime }=-9 x_{1}-3 x_{2}-9 x_{3}+1 \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.873 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2}+x_{3}+t \\ x_{2}^{\prime }=x_{1}-4 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}-3 x_{3}+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.965 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=8 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.477 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+9 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.584 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1} \\ x_{2}^{\prime }=-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.323 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-2 x_{2} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-7 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.556 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.438 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-8 x_{2} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.447 |
|
|
\[
{}y^{\prime }+y = 8 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.429 |
|
|
\[
{}y^{\prime }+3 y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.464 |
|
|
\[
{}y^{\prime }+2 y = 4 t
\] |
[[_linear, ‘class A‘]] |
✓ |
0.365 |
|
|
\[
{}y^{\prime }-y = 6 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.498 |
|
|
\[
{}y^{\prime }-y = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.543 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.316 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.298 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.250 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 36
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.221 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.341 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.324 |
|
|
\[
{}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12-6 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-y = 6 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.377 |
|
|
\[
{}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.391 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.370 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.406 |
|
|
\[
{}y^{\prime \prime }+4 y = 9 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.368 |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.455 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime }+2 y = 2 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.597 |
|
|
\[
{}y^{\prime }-2 y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.670 |
|
|
\[
{}y^{\prime }-y = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.821 |
|
|
\[
{}y^{\prime }+2 y = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.912 |
|
|
\[
{}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.809 |
|
|
\[
{}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
1.102 |
|
|
\[
{}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
82.323 |
|
|
\[
{}y^{\prime \prime }-y = \operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.765 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.080 |
|
|
\[
{}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.655 |
|
|
\[
{}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.662 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.645 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-t +1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.299 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.546 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.938 |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.731 |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.966 |
|
|
\[
{}y^{\prime }+y = \delta \left (t -5\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.504 |
|
|
\[
{}y^{\prime }-2 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.583 |
|
|
\[
{}y^{\prime }+4 y = 3 \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.588 |
|
|
\[
{}y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.695 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.813 |
|
|
\[
{}y^{\prime \prime }-4 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.816 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.958 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.170 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.022 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.178 |
|
|
\[
{}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.899 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.343 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.024 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.368 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\] |
[_erf] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.331 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.295 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.327 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.346 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.354 |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }-3 x y^{\prime }-5 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.387 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.384 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0
\] |
[_Gegenbauer] |
✓ |
0.405 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.383 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.420 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.467 |
|