|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.019 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.345 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.866 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -200
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.268 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.892 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.010 |
|
|
\[
{}y^{\prime \prime }+9 y = 9 x^{4}-9
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.657 |
|
|
\[
{}y^{\prime \prime }+9 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.831 |
|
|
\[
{}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.937 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.297 |
|
|
\[
{}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.682 |
|
|
\[
{}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.727 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.629 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.986 |
|
|
\[
{}y^{\prime \prime }+9 y = 39 x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.453 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.949 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 20
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.520 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime \prime }+9 y = 3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.797 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.973 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.439 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.379 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.991 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.736 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.928 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.715 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.648 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 100
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.037 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.464 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.113 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.974 |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.504 |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.450 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
21.667 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.829 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.219 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.004 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.939 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.106 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.816 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.875 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.996 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
22.530 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
26.866 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.990 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.003 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 12 \,{\mathrm e}^{-2 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 10 \sin \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 \,{\mathrm e}^{4 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 x
\] |
[[_high_order, _missing_y]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.113 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.146 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.714 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.497 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.196 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.601 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.176 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.888 |
|
|
\[
{}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.247 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.594 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.385 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = \frac {5}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.441 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +y = \frac {50}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.802 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 85 \cos \left (2 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.834 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.903 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y = 4 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.968 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.933 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 6 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.661 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 64 x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.813 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.804 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.852 |
|
|
\[
{}y^{\prime \prime }+4 y = \csc \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.533 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.898 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.066 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.047 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \sqrt {x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.888 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 12 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.779 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.609 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.767 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = \frac {1}{x -2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.218 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.707 |
|
|
\[
{}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.900 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.436 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.260 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.571 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.106 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.233 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = {\mathrm e}^{-x^{2}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.342 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \tan \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.023 |
|
|
\[
{}y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.531 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y = 12 x \sin \left (x^{2}\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.366 |
|
|
\[
{}y^{\prime \prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.739 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.750 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.877 |
|
|
\[
{}y^{\prime \prime }-36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.971 |
|