|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.148 |
|
|
\[
{}x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y = 0
\] |
[_Laguerre] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime }+a \left (x y^{\prime }+y\right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.848 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.842 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.959 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.082 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.075 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.970 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.861 |
|
|
\[
{}6 y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.876 |
|
|
\[
{}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.983 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.859 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.020 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.903 |
|
|
\[
{}4 y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.085 |
|
|
\[
{}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.961 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.318 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.571 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.577 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.139 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.104 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.957 |
|
|
\[
{}9 y^{\prime \prime }-24 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.961 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.292 |
|
|
\[
{}4 y^{\prime \prime }+9 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.872 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.062 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.788 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.411 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.259 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.390 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.276 |
|
|
\[
{}6 y^{\prime \prime }-5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.201 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.345 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.892 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.048 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.161 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.390 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.714 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.477 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.648 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.459 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.490 |
|
|
\[
{}4 y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.749 |
|
|
\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.230 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.336 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.233 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.871 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }-6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.957 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.697 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.902 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.688 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.668 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.602 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.973 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.493 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.994 |
|
|
\[
{}y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.375 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.904 |
|
|
\[
{}m y^{\prime \prime }+k y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
10.243 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 3 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.138 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.096 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = -3 t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.200 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3+4 \sin \left (2 t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.210 |
|
|
\[
{}y^{\prime \prime }+9 y = t^{2} {\mathrm e}^{3 t}+6
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.610 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.117 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.146 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.159 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.188 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.157 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = t^{2}+3 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.835 |
|
|
\[
{}y^{\prime \prime }+y = 3 \sin \left (2 t \right )+t \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.773 |
|
|
\[
{}u^{\prime \prime }+w_{0}^{2} u = \cos \left (w t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.639 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = 2 \sinh \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.985 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \cosh \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.338 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 2 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.195 |
|
|
\[
{}y^{\prime \prime }+4 y = t^{2}+3 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.536 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = t \,{\mathrm e}^{t}+4
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.609 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 3 t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.242 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.165 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-t} \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.020 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
74.269 |
|
|
\[
{}y^{\prime \prime }+y = t \left (1+\sin \left (t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.201 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.051 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.003 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 t^{2}+4 t \,{\mathrm e}^{2 t}+t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
31.535 |
|
|
\[
{}y^{\prime \prime }+4 y = t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.358 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.162 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 t \,{\mathrm e}^{-t} \cos \left (2 t \right )-2 t \,{\mathrm e}^{-2 t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
127.983 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-4 y = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.172 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.414 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.507 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 x^{2}+2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.102 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.159 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{-t +\pi } & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.214 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.703 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.386 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 2 \cos \left (w t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.405 |
|