|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}-y+x y^{\prime } = 2 x
\] |
[_linear] |
✓ |
1.556 |
|
|
\[
{}x^{2} y^{\prime }-2 y = 3 x^{2}
\] |
[_linear] |
✓ |
1.326 |
|
|
\[
{}y^{2} y^{\prime } = x
\] |
[_separable] |
✓ |
3.317 |
|
|
\[
{}\csc \left (x \right ) y^{\prime } = \csc \left (y\right )
\] |
[_separable] |
✓ |
2.822 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.604 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 y^{2}}{-2 y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.501 |
|
|
\[
{}2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.974 |
|
|
\[
{}\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
1.330 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.248 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }-2 {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.686 |
|
|
\[
{}y y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.310 |
|
|
\[
{}x y^{\prime \prime }-3 y^{\prime } = 5 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.182 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.834 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.847 |
|
|
\[
{}y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.036 |
|
|
\[
{}2 y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.263 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.850 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.823 |
|
|
\[
{}2 y^{\prime \prime }+2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.083 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.868 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.845 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.838 |
|
|
\[
{}4 y^{\prime \prime }+20 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.875 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.895 |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.081 |
|
|
\[
{}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.157 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.832 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.274 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.273 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.821 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.100 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.402 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.138 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.128 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.523 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.457 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.618 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.135 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.971 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.744 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.158 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.025 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.840 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.198 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.115 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.587 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.042 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
15.478 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.139 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.457 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.855 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 12 x -10
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.618 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.037 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.128 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.585 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.367 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.786 |
|
|
\[
{}y^{\prime \prime }-3 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.191 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.627 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.972 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.159 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.110 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.250 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.005 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.043 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.754 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.427 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.627 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.358 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.935 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.496 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.224 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.014 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.028 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.454 |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.539 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.625 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.319 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.383 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.453 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.386 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.307 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.317 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.342 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.388 |
|
|
\[
{}y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.338 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.309 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.656 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.367 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime \prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|