|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x y^{\prime }-y = 2 x \cos \left (x \right )
\] |
[_linear] |
✓ |
1.679 |
|
|
\[
{}x^{2} y^{\prime }+x y = 10 \sin \left (x \right )
\] |
[_linear] |
✓ |
1.494 |
|
|
\[
{}y^{\prime }+2 x y = 1
\] |
[_linear] |
✓ |
1.144 |
|
|
\[
{}x y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
2.135 |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
4.051 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
1.701 |
|
|
\[
{}5 y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.632 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.860 |
|
|
\[
{}2 y^{\prime \prime }+7 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.879 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.737 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.460 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.866 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.169 |
|
|
\[
{}3 x y^{\prime }+5 y = 10
\] |
[_separable] |
✓ |
2.297 |
|
|
\[
{}y^{\prime } = y^{2}+2 y-3
\] |
[_quadrature] |
✓ |
1.930 |
|
|
\[
{}\left (y-1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
1.740 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 y = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.478 |
|
|
\[
{}{y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
0.368 |
|
|
\[
{}{y^{\prime }}^{2} = 9-y^{2}
\] |
[_quadrature] |
✓ |
0.712 |
|
|
\[
{}y y^{\prime }+\sqrt {16-y^{2}} = 0
\] |
[_quadrature] |
✓ |
2.693 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=5 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.469 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }=4 x-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.027 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
41.661 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.831 |
|
|
\[
{}y^{\prime } = f \left (x \right )
\] |
[_quadrature] |
✓ |
0.175 |
|
|
\[
{}y^{\prime \prime } = f \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.495 |
|
|
\[
{}x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3} = 0
\] |
[_quadrature] |
✓ |
0.303 |
|
|
\[
{}y^{\prime } = 5-y
\] |
[_quadrature] |
✓ |
1.421 |
|
|
\[
{}y^{\prime } = y^{2}+4
\] |
[_quadrature] |
✓ |
4.912 |
|
|
\[
{}y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
2.739 |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
2.802 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.456 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.500 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.487 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.519 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
30.081 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.020 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.729 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.084 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.542 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.292 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.302 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.593 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
2.029 |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_separable] |
✓ |
2.570 |
|
|
\[
{}y^{\prime } = y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
2.008 |
|
|
\[
{}y^{\prime } = \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
9.498 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
1.603 |
|
|
\[
{}y^{\prime }-y = x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.215 |
|
|
\[
{}\left (4-y^{2}\right ) y^{\prime } = x^{2}
\] |
[_separable] |
✓ |
1.320 |
|
|
\[
{}\left (1+y^{3}\right ) y^{\prime } = x^{2}
\] |
[_separable] |
✓ |
1.358 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3714.248 |
|
|
\[
{}\left (y-x \right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.999 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
168.398 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
3.195 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
3.083 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
21.756 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
1.267 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
3.071 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.383 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.771 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.938 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.181 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.707 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
4.698 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
3.918 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
7.868 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.786 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.574 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.812 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.559 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.673 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.736 |
|
|
\[
{}y^{\prime } = x -2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.558 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✗ |
1.559 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.611 |
|
|
\[
{}y^{\prime }+2 y = 3 x -6
\] |
[[_linear, ‘class A‘]] |
✓ |
1.299 |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
6.040 |
|
|
\[
{}x y^{\prime } = 2 x
\] |
[_quadrature] |
✓ |
0.821 |
|
|
\[
{}y^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.801 |
|
|
\[
{}y^{\prime } = 2 y-4
\] |
[_quadrature] |
✓ |
1.469 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
1.619 |
|
|
\[
{}y^{\prime \prime }+9 y = 18
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.550 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.800 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.619 |
|
|
\[
{}y^{\prime } = y \left (y-3\right )
\] |
[_quadrature] |
✓ |
1.940 |
|
|
\[
{}3 x y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
2.223 |
|
|
\[
{}\left (2 y-2\right ) y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
3.845 |
|
|
\[
{}x y^{\prime }+y = 2 x
\] |
[_linear] |
✓ |
1.794 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.440 |
|
|
\[
{}{y^{\prime }}^{2} = 4 x^{2}
\] |
[_quadrature] |
✓ |
0.460 |
|
|
\[
{}y^{\prime } = 6 \sqrt {y}+5 x^{3}
\] |
[_Chini] |
✗ |
1.235 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )-2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.699 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.816 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.059 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = \sec \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.702 |
|
|
\[
{}y^{\prime }+y \sin \left (x \right ) = x
\] |
[_linear] |
✓ |
1.671 |
|