|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.834 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.304 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.379 |
|
|
\[
{}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.574 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.016 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.069 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.837 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.068 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.082 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.346 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.058 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.283 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.289 |
|
|
\[
{}y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.334 |
|
|
\[
{}y^{\prime \prime }+7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.366 |
|
|
\[
{}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.083 |
|
|
\[
{}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.084 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.179 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.174 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.266 |
|
|
\[
{}3 y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.518 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.568 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.388 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.647 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.628 |
|
|
\[
{}y^{\prime \prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.309 |
|
|
\[
{}y^{\prime \prime }+100 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.144 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.495 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.672 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.760 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.743 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.184 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.143 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.747 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.078 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.179 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.987 |
|
|
\[
{}3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.243 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.158 |
|
|
\[
{}a y^{\prime \prime }+2 b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.639 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.430 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.066 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.065 |
|
|
\[
{}y^{\prime \prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.375 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.602 |
|
|
\[
{}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.082 |
|
|
\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.076 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.154 |
|
|
\[
{}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.090 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.286 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.349 |
|
|
\[
{}y^{\prime \prime }-y = 2 t -4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.270 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.379 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3-4 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.226 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.927 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.169 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )+t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.343 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.485 |
|
|
\[
{}y^{\prime \prime } = 3 t^{4}-2 t
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.957 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.467 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.205 |
|
|
\[
{}5 y^{\prime \prime }+y^{\prime }-4 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.234 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.299 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.378 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.462 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.790 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.267 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.451 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.722 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.389 |
|
|
\[
{}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.741 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.749 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.181 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.267 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.487 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.344 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.195 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.315 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.340 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.320 |
|
|
\[
{}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.559 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 18
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.757 |
|
|
\[
{}y^{\prime \prime }-y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.497 |
|
|
\[
{}y^{\prime \prime }-4 y = 32 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.374 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.782 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 3 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.782 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.693 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.681 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = -1
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.270 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.879 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.996 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 2 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.723 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.391 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.815 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.815 |
|
|
\[
{}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
57.293 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.603 |
|
|
\[
{}y^{\prime }-4 y = t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.259 |
|