|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+8 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.211 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.479 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.168 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.468 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.386 |
|
|
\[
{}y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.546 |
|
|
\[
{}y^{\prime \prime }+7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.514 |
|
|
\[
{}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.164 |
|
|
\[
{}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.141 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.278 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.284 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.425 |
|
|
\[
{}3 y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.677 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.745 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.461 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.782 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.763 |
|
|
\[
{}y^{\prime \prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.601 |
|
|
\[
{}y^{\prime \prime }+100 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.400 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.603 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.622 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.209 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.540 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.905 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.462 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.198 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.852 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.139 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.281 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.816 |
|
|
\[
{}3 t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.309 |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.229 |
|
|
\[
{}a y^{\prime \prime }+2 b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.837 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.533 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.131 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.146 |
|
|
\[
{}y^{\prime \prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.532 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.742 |
|
|
\[
{}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.085 |
|
|
\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.077 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.244 |
|
|
\[
{}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.253 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.424 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.485 |
|
|
\[
{}y^{\prime \prime }-y = 2 t -4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.344 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.497 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3-4 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.318 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.009 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.628 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )+t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.639 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.829 |
|
|
\[
{}y^{\prime \prime } = 3 t^{4}-2 t
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.063 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.243 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.239 |
|
|
\[
{}5 y^{\prime \prime }+y^{\prime }-4 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.283 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.393 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.448 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
15.361 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.858 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.347 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.528 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.929 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.005 |
|
|
\[
{}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.994 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.839 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.228 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.332 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.504 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.434 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.272 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.372 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.427 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.290 |
|
|
\[
{}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.569 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 18
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.830 |
|
|
\[
{}y^{\prime \prime }-y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.595 |
|
|
\[
{}y^{\prime \prime }-4 y = 32 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.455 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.812 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 3 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.813 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.779 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.616 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = -1
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.829 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.940 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.055 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 2 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.990 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.405 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.845 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.764 |
|
|
\[
{}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
57.141 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.806 |
|
|
\[
{}y^{\prime }-4 y = t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.241 |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.675 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.587 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.479 |
|
|
\[
{}y^{\prime }+4 y = t \,{\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.899 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.815 |
|
|
\[
{}x^{\prime \prime }+9 x = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.981 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.474 |
|
|
\[
{}y^{\prime \prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.701 |
|
|
\[
{}y^{\prime \prime }+16 y^{\prime } = t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.218 |
|