|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.596 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.317 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.314 |
|
|
\[
{}x^{\prime \prime }+x-x^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.332 |
|
|
\[
{}x^{\prime \prime }+x+x^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.670 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.733 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.728 |
|
|
\[
{}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.456 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.468 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.231 |
|
|
\[
{}-y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.622 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.195 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.058 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.846 |
|
|
\[
{}y^{\prime }+\frac {1}{2 y} = 0
\] |
[_quadrature] |
✓ |
1.652 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
1.490 |
|
|
\[
{}y^{\prime }-2 \sqrt {{| y|}} = 0
\] |
[_quadrature] |
✓ |
1.516 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
2.189 |
|
|
\[
{}y^{\prime }-y^{2} = 1
\] |
[_quadrature] |
✓ |
1.196 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.137 |
|
|
\[
{}y^{\prime } x -\sin \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
0.542 |
|
|
\[
{}y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
1.359 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.084 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}2 y^{\prime } x -y = 0
\] |
[_separable] |
✓ |
2.135 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.734 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.263 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.191 |
|
|
\[
{}{y^{\prime }}^{2}-4 y = 0
\] |
[_quadrature] |
✓ |
0.550 |
|
|
\[
{}{y^{\prime }}^{2}-9 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.521 |
|
|
\[
{}{y^{\prime }}^{2} = x^{6}
\] |
[_quadrature] |
✓ |
0.839 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
1.574 |
|
|
\[
{}y^{\prime }+y = x^{2}+2 x -1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.268 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
2.674 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.190 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.539 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y = 0
\] |
[_separable] |
✓ |
1.753 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.646 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.684 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.160 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.169 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.122 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.947 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.036 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.954 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.941 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.412 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
1.155 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.439 |
|
|
\[
{}y^{\prime } = x -1
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.107 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
1.141 |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
1.567 |
|
|
\[
{}y^{\prime } = 4-y^{2}
\] |
[_quadrature] |
✓ |
1.543 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
1.569 |
|
|
\[
{}y^{\prime } = -x y
\] |
[_separable] |
✓ |
1.809 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.024 |
|
|
\[
{}y^{\prime } = y^{2}-x^{2}
\] |
[_Riccati] |
✓ |
1.015 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.182 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
1.579 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
3.503 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.598 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.187 |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
1.742 |
|
|
\[
{}y^{\prime } = x^{3}+y^{3}
\] |
[_Abel] |
✗ |
0.620 |
|
|
\[
{}y^{\prime } = {| y|}
\] |
[_quadrature] |
✓ |
1.142 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.988 |
|
|
\[
{}y^{\prime } = \ln \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.090 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.591 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.335 |
|
|
\[
{}y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x}
\] |
[_linear] |
✓ |
2.205 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.224 |
|
|
\[
{}y^{\prime } = \frac {1}{x y}
\] |
[_separable] |
✓ |
1.695 |
|
|
\[
{}y^{\prime } = \ln \left (-1+y\right )
\] |
[_quadrature] |
✓ |
1.036 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
28.347 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.190 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
2.362 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.817 |
|
|
\[
{}y^{\prime } = \frac {x y}{1-y}
\] |
[_separable] |
✓ |
1.261 |
|
|
\[
{}y^{\prime } = \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.167 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y-4}{x}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.877 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}+y^{{1}/{4}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
9.791 |
|
|
\[
{}y^{\prime } = 4 y-5
\] |
[_quadrature] |
✓ |
1.556 |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
1.569 |
|
|
\[
{}y^{\prime } = a y+b
\] |
[_quadrature] |
✓ |
0.794 |
|
|
\[
{}y^{\prime } = x^{2}+{\mathrm e}^{x}-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.829 |
|
|
\[
{}y^{\prime } = x y+\frac {1}{x^{2}+1}
\] |
[_linear] |
✓ |
2.220 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cos \left (x \right )
\] |
[_linear] |
✓ |
1.602 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (x \right )
\] |
[_linear] |
✓ |
2.171 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
2.743 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
2.480 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) y+\csc \left (x \right )
\] |
[_linear] |
✓ |
1.801 |
|
|
\[
{}y^{\prime } = -x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
3.883 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.490 |
|
|
\[
{}y^{\prime } = 3 x +1
\] |
[_quadrature] |
✓ |
0.607 |
|
|
\[
{}y^{\prime } = x +\frac {1}{x}
\] |
[_quadrature] |
✓ |
0.687 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.767 |
|
|
\[
{}y^{\prime } = x \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.794 |
|