|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.055 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.055 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.057 |
|
|
\[
{}y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.759 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.207 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.106 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.133 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 4 x^{2}+5
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.188 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 4 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 24 \,{\mathrm e}^{-3 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = 6 \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime }+y = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.834 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 5 x \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.239 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.670 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.204 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.138 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 4 x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 9 \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.882 |
|
|
\[
{}y^{\prime \prime }-y = 9 x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.219 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.639 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 4 \cos \left (x \right )-2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.539 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.786 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
16.249 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 4 x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime } = 5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.178 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.912 |
|
|
\[
{}y^{\prime \prime }+6 y = \sin \left (x \right )^{2} \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.600 |
|
|
\[
{}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.573 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.501 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.551 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.738 |
|
|
\[
{}y^{\prime \prime }+y = 3 \,{\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.536 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.338 |
|
|
\[
{}y^{\prime \prime }-4 y = 100 x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.737 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
19.632 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
22.145 |
|
|
\[
{}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.624 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.384 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.310 |
|
|
\[
{}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.917 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.844 |
|
|
\[
{}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.408 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
39.869 |
|
|
\[
{}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.397 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.781 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
42.469 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )+4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.915 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.894 |
|
|
\[
{}y^{\prime \prime }-y = 2 \tanh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.787 |
|
|
\[
{}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \frac {{\mathrm e}^{m x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.908 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.361 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.566 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
104.205 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.266 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {2 \,{\mathrm e}^{x}}{x^{2}}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.282 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 36 \,{\mathrm e}^{2 x} \ln \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = \frac {2 \,{\mathrm e}^{-x}}{x^{2}+1}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.363 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 12 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime }-9 y = F \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.521 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.549 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = F \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.548 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = F \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.568 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 5 x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.580 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.418 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.010 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.312 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.582 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
48.902 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.020 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.851 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.531 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.886 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.278 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.878 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.086 |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.097 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.148 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.099 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.155 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.484 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.299 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.257 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.441 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.451 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.188 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.057 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.243 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.243 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = \sin \left (4 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.159 |
|