|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.888 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.257 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.060 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.599 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.467 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.540 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.525 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.600 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.150 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.103 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.736 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.756 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.888 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.621 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.639 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 12 \,{\mathrm e}^{-2 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.168 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 10 \sin \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.201 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 \,{\mathrm e}^{4 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.162 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 x
\] |
[[_high_order, _missing_y]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.144 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.201 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.166 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.203 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.950 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.528 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.263 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.820 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.259 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.199 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.012 |
|
|
\[
{}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.414 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.764 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.862 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = \frac {5}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.529 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +y = \frac {50}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.864 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 85 \cos \left (2 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
3.612 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.690 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y = 4 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.901 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.129 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 6 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.636 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 64 x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.539 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.827 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.847 |
|
|
\[
{}y^{\prime \prime }+4 y = \csc \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.101 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.560 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.640 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.674 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \sqrt {x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.155 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 12 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.816 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.535 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.491 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = \frac {1}{x -2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.937 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.647 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.298 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.975 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.160 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.761 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.158 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.275 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = {\mathrm e}^{-x^{2}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.419 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \tan \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.005 |
|
|
\[
{}y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.630 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y = 12 x \sin \left (x^{2}\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.496 |
|
|
\[
{}y^{\prime \prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.442 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.399 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.889 |
|
|
\[
{}y^{\prime \prime }-36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.537 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.375 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.862 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.999 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.479 |
|
|
\[
{}y^{\prime \prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.573 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.910 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {5 y}{2} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.511 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.093 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.559 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.543 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.973 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.569 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.782 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.353 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.416 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.899 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.149 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.918 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.955 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }+3 = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.237 |
|
|
\[
{}y^{\prime \prime }+20 y^{\prime }+100 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.410 |
|
|
\[
{}x y^{\prime \prime } = 3 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.130 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.026 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.479 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.840 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.549 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.600 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.808 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.672 |
|
|
\[
{}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.375 |
|