|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 3 x^{2} \left (7+y\right )
\] |
[_separable] |
✓ |
1.546 |
|
|
\[
{}y^{\prime } = -x y+x y^{3}
\] |
[_separable] |
✓ |
4.239 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
98.419 |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{-3 x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.566 |
|
|
\[
{}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1}
\] |
[_separable] |
✓ |
1.570 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) \left (\sqrt {y}-y\right )
\] |
[_separable] |
✓ |
8.656 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.300 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.585 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.238 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
17.937 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.157 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.417 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.485 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.419 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.350 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.373 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.133 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.855 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.835 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.087 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.754 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.548 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.827 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.866 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.883 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.904 |
|
|
\[
{}2 y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.859 |
|
|
\[
{}4 y^{\prime \prime }+8 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.877 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.990 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.963 |
|
|
\[
{}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.856 |
|
|
\[
{}35 y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.854 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.210 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.749 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.766 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.521 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.877 |
|
|
\[
{}y^{\prime \prime }+y = 3 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.162 |
|
|
\[
{}y^{\prime \prime }-4 y = 12
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.904 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.576 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.457 |
|
|
\[
{}y^{\prime \prime }+2 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.700 |
|
|
\[
{}y^{\prime \prime }+2 y = 6 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.889 |
|
|
\[
{}y^{\prime \prime }+2 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.019 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.970 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.819 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.858 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.875 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.962 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.116 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.975 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.614 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.712 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.400 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.859 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.418 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.624 |
|
|
\[
{}y^{\prime \prime }-i y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.561 |
|
|
\[
{}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.655 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.285 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
34.407 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.188 |
|
|
\[
{}3 x^{\prime \prime }+30 x^{\prime }+63 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.415 |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.374 |
|
|
\[
{}2 x^{\prime \prime }+12 x^{\prime }+50 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.062 |
|
|
\[
{}4 x^{\prime \prime }+20 x^{\prime }+169 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.987 |
|
|
\[
{}2 x^{\prime \prime }+16 x^{\prime }+40 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.865 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+125 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.239 |
|
|
\[
{}y^{\prime \prime }+16 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.342 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 3 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.130 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.486 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.236 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.459 |
|
|
\[
{}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
23.960 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.947 |
|
|
\[
{}y^{\prime \prime }-4 y = \cosh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.977 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.274 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.128 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.423 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.312 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.879 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.319 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
23.539 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.408 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.615 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.387 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.867 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.596 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (x \right )^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.953 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.793 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.078 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.155 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.142 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.154 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.959 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.697 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.370 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.448 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.560 |
|