|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.579 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 3 x^{{3}/{2}} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.530 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = g \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.528 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.448 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.057 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.649 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.850 |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.638 |
|
|
\[
{}y^{\prime \prime }+y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.853 |
|
|
\[
{}t y^{\prime \prime }-\left (1+t \right ) y^{\prime }-y = t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.418 |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.428 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.332 |
|
|
\[
{}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.247 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.239 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.243 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = t^{2} {\mathrm e}^{t}+7
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = t^{2}+7
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.275 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.367 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = t \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.390 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y = t \,{\mathrm e}^{-t}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.763 |
|
|
\[
{}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.749 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.738 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.632 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.268 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.280 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.236 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.443 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+29 y = {\mathrm e}^{-2 t} \sin \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.424 |
|
|
\[
{}y^{\prime \prime }+w^{2} y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.277 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 18 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.255 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.314 |
|
|
\[
{}y^{\prime \prime \prime \prime }-9 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-5 y_{1}+y_{2} \\ y_{2}^{\prime }=-9 y_{1}+5 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.421 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }=6 y_{1}-2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.418 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-4 y_{2} \\ y_{2}^{\prime }=5 y_{1}-4 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.456 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=6 y_{2} \\ y_{2}^{\prime }=-6 y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-64 y_{2} \\ y_{2}^{\prime }=y_{1}-14 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.416 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\ y_{2}^{\prime }=y_{1}-2 y_{2}+\sin \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.351 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\ y_{2}^{\prime }=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.299 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-5 y_{2}+3 \\ y_{2}^{\prime }=y_{1}+3 y_{2}+5 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.321 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.314 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-y_{3} \\ y_{2}^{\prime }=y_{1}+y_{3}-{\mathrm e}^{-t} \\ y_{3}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.242 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.631 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.587 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.495 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.552 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.757 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.478 |
|
|
\[
{}y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.420 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.468 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.638 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.605 |
|
|
\[
{}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.761 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
3.573 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.888 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.025 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.961 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = 2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.062 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.570 |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.457 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.789 |
|
|
\[
{}y^{\prime \prime }-y = -20 \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.514 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.611 |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -4 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.497 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.468 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.438 |
|
|
\[
{}y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.874 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }+6 y = \delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.879 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \delta \left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.813 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.783 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.772 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{5}+y = k \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.704 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{10}+y = k \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.666 |
|
|
\[
{}y^{\prime \prime }+w^{2} y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.684 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = \sin \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.433 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+17 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.352 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.450 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.633 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.382 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = g \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.993 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = g \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
3.622 |
|
|
\[
{}\frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.328 |
|
|
\[
{}\frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.337 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+3 y = t
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.138 |
|
|
\[
{}t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.069 |
|
|
\[
{}t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y = \ln \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.062 |
|
|
\[
{}\left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.070 |
|
|
\[
{}\left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.059 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.120 |
|