|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.689 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.707 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.251 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.895 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.658 |
|
|
\[
{}y^{\prime \prime }-y = 3 x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.319 |
|
|
\[
{}y^{\prime \prime }+y = 3 x^{2}-4 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.345 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.990 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.393 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.218 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.310 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.180 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.579 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
66.201 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
149.542 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{x}+3 x \,{\mathrm e}^{2 x}+5 x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.250 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.323 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
34.496 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime } = x^{3}+x^{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
35.161 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.905 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.391 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = \cos \left (x \right )^{2}-\cosh \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.980 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.152 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.521 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.816 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.954 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.567 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right ) \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.967 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.162 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \tan \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
46.968 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.329 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.419 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.555 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.076 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{x}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.748 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{2 x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.822 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
38.087 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \arcsin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.451 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.302 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \ln \left (x \right ) x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.575 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.320 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.450 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.486 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.338 |
|
|
\[
{}x \left (-2+x \right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (-1+x \right ) y = 3 x^{2} \left (-2+x \right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.625 |
|
|
\[
{}\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.749 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.056 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} {\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.121 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.015 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.837 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.901 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.881 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.367 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
23.164 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.937 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.349 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.880 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.435 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.111 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.111 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.381 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.278 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.036 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 \ln \left (x \right ) x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.040 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.210 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.288 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.463 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.833 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.661 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 4 x -8
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.325 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.235 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.488 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.622 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.198 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }-\left (x +2\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.855 |
|
|
\[
{}\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.931 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.315 |
|
|
\[
{}y^{\prime \prime }+8 x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+\left (3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.385 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.411 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.417 |
|
|
\[
{}\left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.392 |
|
|
\[
{}\left (x +3\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.399 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.319 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.408 |
|
|
\[
{}\left (2 x^{2}-3\right ) y^{\prime \prime }-2 x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.366 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.425 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.457 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.406 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.572 |
|
|
\[
{}\left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.729 |
|
|
\[
{}\left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.885 |
|