|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.013 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}+x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.986 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = x^{2}+x
\] |
[[_high_order, _missing_y]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime }+y = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.960 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.345 |
|
|
\[
{}y^{\prime \prime \prime }-y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.124 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.125 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.967 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.576 |
|
|
\[
{}y^{\prime \prime }-y = x +\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.740 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = \left (1+\sin \left (x \right )\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.398 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } = 1+{\mathrm e}^{x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.413 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.168 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.988 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.027 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.249 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.374 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.860 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
21.342 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.628 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.265 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.261 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.662 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime } = {\mathrm e}^{x}+3 \sin \left (2 x \right )+1
\] |
[[_high_order, _missing_y]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
24.441 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.646 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.357 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.880 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.171 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.510 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.842 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.647 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.572 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.438 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x +\sin \left (x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.050 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.231 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
55.499 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.479 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.229 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 2 x +{\mathrm e}^{x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.747 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 4 x +3 \sin \left (x \right )+\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.128 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = x \,{\mathrm e}^{x}-1
\] |
[[_high_order, _missing_y]] |
✓ |
0.150 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = x +2 \,{\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime }+y = -2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.899 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.339 |
|
|
\[
{}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.550 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.188 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.253 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.745 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.502 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.749 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.912 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.059 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.649 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.266 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\sin \left (x \right )+\cos \left (x \right )\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.491 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.463 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = -2 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime \prime }-y = 2 x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.160 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.183 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.091 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.521 |
|
|
\[
{}y^{\prime \prime }-y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.114 |
|
|
\[
{}y^{\prime \prime }-y = -2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.253 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.175 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.208 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-5 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.645 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.929 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.250 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.437 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.163 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.125 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.219 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.850 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.995 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.969 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.161 |
|
|
\[
{}x^{2} y^{\prime \prime \prime } = 2 y^{\prime }
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.143 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.253 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.655 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = x \left (6-\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
56.848 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.724 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = -\frac {16 \ln \left (x \right )}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.680 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y = x^{2}-2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
123.791 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.023 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 2 \ln \left (x \right )^{2}+12 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.470 |
|
|
\[
{}\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y = 6 \ln \left (x +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
48.061 |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.921 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.092 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
1.271 |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.464 |
|
|
\[
{}x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.313 |
|