|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-9 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.348 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.256 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.187 |
|
|
\[
{}9 y^{\prime \prime }-24 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.193 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.266 |
|
|
\[
{}4 y^{\prime \prime }+9 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.093 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.536 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.924 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.646 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.918 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.345 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.300 |
|
|
\[
{}6 y^{\prime \prime }-5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.368 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.484 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.135 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.450 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.253 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.526 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.849 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.358 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.773 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.683 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.424 |
|
|
\[
{}4 y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.781 |
|
|
\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.287 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.348 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.278 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.962 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x -6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.181 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.847 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.076 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.725 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.738 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.831 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +17 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.771 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.672 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.456 |
|
|
\[
{}y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.059 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.859 |
|
|
\[
{}m y^{\prime \prime }+k y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
24.995 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 3 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.280 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.362 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = -3 t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.418 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3+4 \sin \left (2 t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.216 |
|
|
\[
{}y^{\prime \prime }+9 y = t^{2} {\mathrm e}^{3 t}+6
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.616 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.347 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.335 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.299 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.369 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.375 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = t^{2}+3 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.118 |
|
|
\[
{}y^{\prime \prime }+y = 3 \sin \left (2 t \right )+t \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.829 |
|
|
\[
{}u^{\prime \prime }+w_{0}^{2} u = \cos \left (w t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.648 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = 2 \sinh \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
26.737 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \cosh \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.470 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 2 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.338 |
|
|
\[
{}y^{\prime \prime }+4 y = t^{2}+3 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.387 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = t \,{\mathrm e}^{t}+4
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.845 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 3 t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.468 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.266 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-t} \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.630 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
73.302 |
|
|
\[
{}y^{\prime \prime }+y = t \left (1+\sin \left (t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.474 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.452 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.419 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 t^{2}+4 t \,{\mathrm e}^{2 t}+t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.787 |
|
|
\[
{}y^{\prime \prime }+4 y = t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.833 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.456 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 t \,{\mathrm e}^{-t} \cos \left (2 t \right )-2 t \,{\mathrm e}^{-2 t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
94.791 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-4 y = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.381 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.701 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.649 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 3 x^{2}+2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.217 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.146 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.243 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.817 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.688 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 2 \cos \left (w t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.358 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (w t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.437 |
|
|
\[
{}y^{\prime \prime }+y = 3 \cos \left (w t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.670 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (\frac {t}{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.442 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.361 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (6 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.782 |
|
|
\[
{}y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\] |
[NONE] |
✗ |
0.441 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\] |
[NONE] |
✗ |
0.322 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.251 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.374 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.373 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.387 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.079 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \sec \left (2 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.752 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.635 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \csc \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.391 |
|
|
\[
{}4 y^{\prime \prime }+y = 2 \sec \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
72.149 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.456 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.654 |
|
|
\[
{}y^{\prime \prime }+4 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.851 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.505 |
|
|
\[
{}t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.219 |
|