|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 y^{\prime } x -y = 2 x \cos \left (x \right )
\] |
[_linear] |
✓ |
1.595 |
|
|
\[
{}x^{2} y^{\prime }+x y = 10 \sin \left (x \right )
\] |
[_linear] |
✓ |
1.529 |
|
|
\[
{}y^{\prime }+2 x y = 1
\] |
[_linear] |
✓ |
1.055 |
|
|
\[
{}y^{\prime } x -2 y = 0
\] |
[_separable] |
✓ |
2.223 |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
3.392 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
1.397 |
|
|
\[
{}5 y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.401 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.096 |
|
|
\[
{}2 y^{\prime \prime }+7 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.128 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.906 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.772 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.143 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.205 |
|
|
\[
{}3 y^{\prime } x +5 y = 10
\] |
[_separable] |
✓ |
2.209 |
|
|
\[
{}y^{\prime } = y^{2}+2 y-3
\] |
[_quadrature] |
✓ |
1.688 |
|
|
\[
{}\left (-1+y\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
1.261 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 y = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
6.608 |
|
|
\[
{}{y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
0.578 |
|
|
\[
{}{y^{\prime }}^{2} = 9-y^{2}
\] |
[_quadrature] |
✓ |
0.590 |
|
|
\[
{}y y^{\prime }+\sqrt {16-y^{2}} = 0
\] |
[_quadrature] |
✓ |
6.524 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.414 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=5 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.418 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }=4 x-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
39.312 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.803 |
|
|
\[
{}y^{\prime } = f \left (x \right )
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}y^{\prime \prime } = f \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.646 |
|
|
\[
{}x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3} = 0
\] |
[_quadrature] |
✓ |
0.275 |
|
|
\[
{}y^{\prime } = 5-y
\] |
[_quadrature] |
✓ |
1.180 |
|
|
\[
{}y^{\prime } = y^{2}+4
\] |
[_quadrature] |
✓ |
1.242 |
|
|
\[
{}y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
2.417 |
|
|
\[
{}y^{\prime } = y-y^{2}
\] |
[_quadrature] |
✓ |
2.395 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.414 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.432 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.530 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.439 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.209 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.897 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.372 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.347 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.851 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.865 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.835 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.973 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.654 |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
2.750 |
|
|
\[
{}y^{\prime } = y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.505 |
|
|
\[
{}y^{\prime } = \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
7.123 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.647 |
|
|
\[
{}y^{\prime }-y = x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.202 |
|
|
\[
{}\left (4-y^{2}\right ) y^{\prime } = x^{2}
\] |
[_separable] |
✓ |
1.319 |
|
|
\[
{}\left (1+y^{3}\right ) y^{\prime } = x^{2}
\] |
[_separable] |
✓ |
1.302 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.402 |
|
|
\[
{}\left (y-x \right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.743 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
7.032 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
3.071 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
3.084 |
|
|
\[
{}y^{\prime } = \sqrt {y^{2}-9}
\] |
[_quadrature] |
✓ |
5.366 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.283 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.467 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.525 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.530 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.493 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.507 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.561 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
5.050 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
4.815 |
|
|
\[
{}y y^{\prime } = 3 x
\] |
[_separable] |
✓ |
4.911 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.122 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.826 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.918 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.875 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.322 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.995 |
|
|
\[
{}y^{\prime } = x -2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✗ |
1.438 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.798 |
|
|
\[
{}y^{\prime }+2 y = 3 x -6
\] |
[[_linear, ‘class A‘]] |
✓ |
1.254 |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
5.447 |
|
|
\[
{}y^{\prime } x = 2 x
\] |
[_quadrature] |
✓ |
0.752 |
|
|
\[
{}y^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.800 |
|
|
\[
{}y^{\prime } = 2 y-4
\] |
[_quadrature] |
✓ |
1.210 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.654 |
|
|
\[
{}y^{\prime \prime }+9 y = 18
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.759 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.973 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.784 |
|
|
\[
{}y^{\prime } = y \left (y-3\right )
\] |
[_quadrature] |
✓ |
1.813 |
|
|
\[
{}3 y^{\prime } x -2 y = 0
\] |
[_separable] |
✓ |
2.264 |
|
|
\[
{}\left (2 y-2\right ) y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
4.163 |
|
|
\[
{}y^{\prime } x +y = 2 x
\] |
[_linear] |
✓ |
1.599 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.444 |
|
|
\[
{}{y^{\prime }}^{2} = 4 x^{2}
\] |
[_quadrature] |
✓ |
0.828 |
|
|
\[
{}y^{\prime } = 6 \sqrt {y}+5 x^{3}
\] |
[_Chini] |
✗ |
1.227 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )-2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.884 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.993 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.292 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \sec \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.853 |
|
|
\[
{}y^{\prime }+y \sin \left (x \right ) = x
\] |
[_linear] |
✓ |
1.937 |
|