|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.227 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.454 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.095 |
|
|
\[
{}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.598 |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.613 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.329 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+24 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.855 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.211 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.613 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.239 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.253 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.338 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.241 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.498 |
|
|
\[
{}y^{\prime \prime }+49 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.299 |
|
|
\[
{}t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.080 |
|
|
\[
{}t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.083 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.144 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.079 |
|
|
\[
{}a y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.914 |
|
|
\[
{}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.757 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.083 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.209 |
|
|
\[
{}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.953 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.861 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.843 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.892 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.886 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.148 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.895 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.421 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.303 |
|
|
\[
{}y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.370 |
|
|
\[
{}y^{\prime \prime }+7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.459 |
|
|
\[
{}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.908 |
|
|
\[
{}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.895 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.000 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.007 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.231 |
|
|
\[
{}3 y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.599 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.476 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.216 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.476 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.466 |
|
|
\[
{}y^{\prime \prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
19.283 |
|
|
\[
{}y^{\prime \prime }+100 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.253 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.401 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.020 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.475 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.711 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.204 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.155 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.585 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.885 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.999 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.651 |
|
|
\[
{}3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.152 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.064 |
|
|
\[
{}a y^{\prime \prime }+2 b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.912 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.244 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.888 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.900 |
|
|
\[
{}y^{\prime \prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.118 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.514 |
|
|
\[
{}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.048 |
|
|
\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.046 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.092 |
|
|
\[
{}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.009 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.156 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.241 |
|
|
\[
{}y^{\prime \prime }-y = 2 t -4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.159 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.223 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3-4 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.239 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.829 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.342 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )+t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.821 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.341 |
|
|
\[
{}y^{\prime \prime } = 3 t^{4}-2 t
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.896 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
20.851 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.107 |
|
|
\[
{}5 y^{\prime \prime }+y^{\prime }-4 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.125 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.171 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.247 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
17.122 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.654 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.159 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.328 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.835 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.544 |
|
|
\[
{}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.880 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.625 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.299 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.158 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.335 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.269 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.319 |
|