|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.255 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.291 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.289 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.331 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.646 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.297 |
|
|
\[
{}y^{\prime \prime }-20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.260 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.270 |
|
|
\[
{}3 y^{\prime \prime }+8 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.306 |
|
|
\[
{}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.330 |
|
|
\[
{}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.282 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+34 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.277 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.404 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.354 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.368 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.363 |
|
|
\[
{}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.493 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|
|
\[
{}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.315 |
|
|
\[
{}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.516 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.272 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.368 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.563 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.258 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = t +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.370 |
|
|
\[
{}2 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.317 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.426 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.297 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.417 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.278 |
|
|
\[
{}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.398 |
|
|
\[
{}y^{\prime }-2 y = 4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.719 |
|
|
\[
{}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.514 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.670 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.489 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.773 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.308 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (-4+t \right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.611 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.940 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.144 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.634 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.770 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.639 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.687 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.357 |
|
|
\[
{}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.725 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.523 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.156 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.506 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.351 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.369 |
|
|
\[
{}10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.595 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y = 8
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.426 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 4 t
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.348 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
1.844 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
9.901 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
5.250 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.805 |
|
|
\[
{}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
476.443 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.512 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.258 |
|
|
\[
{}t^{3} y^{\prime \prime }-2 t y^{\prime }+y = t^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.532 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.957 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.653 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-7 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.588 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 5
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.380 |
|
|
\[
{}y^{\prime \prime \prime } = 2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.141 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.333 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=\frac {x}{2}-\frac {3 y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+2 y=0 \\ y^{\prime }+y-x=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.368 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x-2 y=0 \\ 2 x+y^{\prime }-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.525 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-3 x+2 y=0 \\ y^{\prime }-x+3 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.491 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x-z=0 \\ x+y^{\prime }-y=0 \\ z^{\prime }+x+2 y-3 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2}+2 y-3 z \\ y^{\prime }=y-\frac {z}{2} \\ z^{\prime }=-2 x+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.889 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }=y \\ x^{\prime }-y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.353 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y^{\prime }=t \\ x^{\prime }-y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }=x+y-t \\ 2 x^{\prime }+3 y^{\prime }=2 x+6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }-y^{\prime }=t \\ 3 x^{\prime }+2 y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}\left [\begin {array}{c} 5 x^{\prime }-3 y^{\prime }=x+y \\ 3 x^{\prime }-y^{\prime }=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.469 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-4 y^{\prime }=0 \\ 2 x^{\prime }-3 y^{\prime }=y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.361 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }=\sin \left (t \right ) \\ x^{\prime }-2 y^{\prime }=x+y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.631 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+9 y+12 \,{\mathrm e}^{-t} \\ y^{\prime }=-5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.661 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+6 y+6 \,{\mathrm e}^{-t} \\ y^{\prime }=-12 x+5 y+37 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.743 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+10 y+18 \,{\mathrm e}^{t} \\ y^{\prime }=-10 x+9 y+37 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.002 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-14 x+39 y+78 \sinh \left (t \right ) \\ y^{\prime }=-6 x+16 y+6 \cosh \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.223 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y-2 z-2 \sinh \left (t \right ) \\ y^{\prime }=4 x+2 y-2 z+10 \cosh \left (t \right ) \\ z^{\prime }=-x+3 y+z+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.034 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\ y^{\prime }=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\ z^{\prime }=-x+6 y+z+9 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.918 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y+4 z \\ y^{\prime }=-2 x+y+2 z \\ z^{\prime }=-4 x-2 y+6 z+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y+3 z \\ y^{\prime }=x-y+2 z+2 \,{\mathrm e}^{-t} \\ z^{\prime }=-2 x+2 y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.835 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y-1-6 \,{\mathrm e}^{t} \\ y^{\prime }=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.617 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y+24 \sin \left (t \right ) \\ y^{\prime }=9 x-3 y+12 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.922 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y+10 \,{\mathrm e}^{t} \\ y^{\prime }=3 x+14 y+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.635 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\ y^{\prime }=-5 x+2 y+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.638 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-3 y+z \\ y^{\prime }=2 y+2 z+29 \,{\mathrm e}^{-t} \\ z^{\prime }=5 x+y+z+39 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
25.812 |
|