|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 3 x^{2} \left (7+y\right )
\] |
[_separable] |
✓ |
0.761 |
|
|
\[
{}y^{\prime } = -y x +x y^{3}
\] |
[_separable] |
✓ |
5.549 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 y x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
82.192 |
|
|
\[
{}y^{\prime } = \frac {x +3 y}{y-3 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.329 |
|
|
\[
{}y^{\prime } = \frac {2 y x +2 x}{x^{2}+1}
\] |
[_separable] |
✓ |
1.130 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) \left (\sqrt {y}-y\right )
\] |
[_separable] |
✓ |
12.847 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.718 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.115 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.645 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.230 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.574 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.561 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.459 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.040 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.722 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.718 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.023 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.728 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
3.324 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.014 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.404 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
3.149 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.362 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.033 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.103 |
|
|
\[
{}2 y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.393 |
|
|
\[
{}4 y^{\prime \prime }+8 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.385 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.064 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.438 |
|
|
\[
{}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.418 |
|
|
\[
{}35 y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.438 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.199 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.719 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.408 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.460 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.904 |
|
|
\[
{}y^{\prime \prime }+y = 3 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.965 |
|
|
\[
{}y^{\prime \prime }-4 y = 12
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.156 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.767 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.119 |
|
|
\[
{}y^{\prime \prime }+2 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.598 |
|
|
\[
{}y^{\prime \prime }+2 y = 6 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.589 |
|
|
\[
{}y^{\prime \prime }+2 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.461 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.877 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.065 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.378 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.405 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.413 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.677 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.408 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.493 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.597 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.612 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.876 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.670 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.530 |
|
|
\[
{}y^{\prime \prime }-i y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.497 |
|
|
\[
{}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.040 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.231 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.307 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.308 |
|
|
\[
{}3 x^{\prime \prime }+30 x^{\prime }+63 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.602 |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.713 |
|
|
\[
{}2 x^{\prime \prime }+12 x^{\prime }+50 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.627 |
|
|
\[
{}4 x^{\prime \prime }+20 x^{\prime }+169 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.859 |
|
|
\[
{}2 x^{\prime \prime }+16 x^{\prime }+40 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.452 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+125 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.943 |
|
|
\[
{}y^{\prime \prime }+16 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.310 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 3 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.432 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.136 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.682 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.655 |
|
|
\[
{}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
19.247 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.470 |
|
|
\[
{}y^{\prime \prime }-4 y = \cosh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.154 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.820 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.279 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.557 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.658 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.438 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.761 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
35.920 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.644 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.759 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.131 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.458 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.876 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
93.720 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (x \right )^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.312 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.333 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.561 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.600 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.567 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.708 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.834 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.224 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.916 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.911 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.710 |
|