|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.307 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.289 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
10.207 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.111 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.356 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.780 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.282 |
|
|
\[
{}y^{\prime \prime }-y = 3 x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.334 |
|
|
\[
{}y^{\prime \prime }+y = 3 x^{2}-4 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.791 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.035 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.199 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.195 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.402 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.487 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
65.093 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
123.867 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{x}+3 x \,{\mathrm e}^{2 x}+5 x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.238 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.237 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.079 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
34.384 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime } = x^{3}+x^{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
35.404 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.543 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = \cos \left (x \right )^{2}-\cosh \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.921 |
|
|
\[
{}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.128 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.869 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.068 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.174 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.624 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.172 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.395 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.205 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \tan \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.934 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.009 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.047 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.999 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.454 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{x}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.847 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.330 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{1+\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.684 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \arcsin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.143 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.231 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.253 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y^{\prime } x +10 y = 3 x^{4}+6 x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.418 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.425 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.544 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.613 |
|
|
\[
{}\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = \left (2 x +1\right )^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.658 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.844 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} {\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.124 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.071 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.907 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.962 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.964 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.174 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.018 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.004 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.174 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.982 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.734 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.115 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 y^{\prime } x +18 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 4 x -6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.437 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.339 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 4 \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.007 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 2 x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
56.072 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 4 \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.869 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.228 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.539 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.855 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.650 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 4 x -8
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.354 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y = -6 x^{3}+4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.301 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 10 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.611 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.677 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.297 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }-\left (x +2\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.937 |
|
|
\[
{}\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.900 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.523 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.497 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.492 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.531 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +\left (3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.565 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.598 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.610 |
|
|
\[
{}\left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.593 |
|
|
\[
{}\left (x +3\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.592 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.464 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.468 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.601 |
|
|
\[
{}\left (2 x^{2}-3\right ) y^{\prime \prime }-2 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.575 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.625 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.645 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.604 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.693 |
|
|
\[
{}\left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.871 |
|