|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.048 |
|
|
\[
{}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.127 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.477 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.222 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = \frac {5}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.634 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +y = \frac {50}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.958 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 85 \cos \left (2 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
3.255 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.216 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y = 4 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.069 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.177 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 6 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.760 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 64 x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.783 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.848 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.266 |
|
|
\[
{}y^{\prime \prime }+4 y = \csc \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.470 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.288 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.405 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.531 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \sqrt {x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.020 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 12 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.827 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.669 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.747 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = \frac {1}{x -2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.131 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.280 |
|
|
\[
{}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.966 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.440 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.484 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.839 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.115 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.237 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = {\mathrm e}^{-x^{2}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.354 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \tan \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.036 |
|
|
\[
{}y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.535 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y = 12 x \sin \left (x^{2}\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.410 |
|
|
\[
{}y^{\prime \prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.273 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.173 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.975 |
|
|
\[
{}y^{\prime \prime }-36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.410 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.062 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.084 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.108 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.174 |
|
|
\[
{}y^{\prime \prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.353 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.078 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {5 y}{2} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.985 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.681 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.021 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.285 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.350 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.047 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.925 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.074 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.182 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.086 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.114 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.201 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }+3 = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.156 |
|
|
\[
{}y^{\prime \prime }+20 y^{\prime }+100 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.177 |
|
|
\[
{}x y^{\prime \prime } = 3 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.954 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.867 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.461 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.758 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.396 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.385 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.767 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.402 |
|
|
\[
{}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.502 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 18 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.536 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.382 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x -2 y = 10 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.556 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.733 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = -3 x {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.756 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.280 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \frac {1}{x^{2}+1}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.227 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.395 |
|
|
\[
{}3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.784 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = {\mathrm e}^{-2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.124 |
|
|
\[
{}y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.160 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{\left (x +1\right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.888 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.716 |
|
|
\[
{}y^{\prime }+4 y = 0
\] |
[_quadrature] |
✓ |
0.363 |
|
|
\[
{}y^{\prime }-2 y = t^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.421 |
|
|
\[
{}y^{\prime }+3 y = \operatorname {Heaviside}\left (t -4\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.461 |
|
|
\[
{}y^{\prime \prime }-4 y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.266 |
|
|
\[
{}y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.311 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.330 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.607 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.272 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 7
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.252 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.424 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.498 |
|
|
\[
{}y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.561 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.278 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.250 |
|
|
\[
{}y^{\prime \prime }+9 y = 27 t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.311 |
|