|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.151 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.122 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.334 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.363 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
35.477 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.385 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.428 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 12 \,{\mathrm e}^{-2 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 10 \sin \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 \,{\mathrm e}^{4 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 x
\] |
[[_high_order, _missing_y]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.111 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.157 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.161 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.988 |
|
|
\[
{}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.620 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.801 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.160 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.213 |
|
|
\[
{}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.608 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
22.615 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.179 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.586 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.180 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
4.003 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.767 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.300 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.439 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.817 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.872 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.985 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.537 |
|
|
\[
{}y^{\prime \prime }+4 y = \csc \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.003 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.295 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.401 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.571 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.363 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.012 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.598 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.739 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = \frac {1}{-2+x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.566 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.411 |
|
|
\[
{}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.884 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.622 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.586 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.784 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.107 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.319 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = {\mathrm e}^{-x^{2}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.445 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \tan \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.966 |
|
|
\[
{}y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.748 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 12 x \sin \left (x^{2}\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.449 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.029 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.935 |
|
|
\[
{}y^{\prime \prime }-36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.234 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.927 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.024 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.191 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.020 |
|
|
\[
{}y^{\prime \prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.516 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.973 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {5 y}{2} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.683 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.467 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.035 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.408 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.478 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.068 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.853 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.930 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.052 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.000 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.032 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.003 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }+3 = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.210 |
|
|
\[
{}y^{\prime \prime }+20 y^{\prime }+100 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.046 |
|
|
\[
{}x y^{\prime \prime } = 3 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.915 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.966 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.397 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.679 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.349 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.388 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.981 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.428 |
|
|
\[
{}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.102 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.577 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.382 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.675 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.765 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = -3 x {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.942 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
272.364 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.409 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.302 |
|