|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}2 x y^{\prime }-y = 0
\] |
[_separable] |
✓ |
1.692 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.754 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.279 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.200 |
|
|
\[
{}{y^{\prime }}^{2}-4 y = 0
\] |
[_quadrature] |
✓ |
0.582 |
|
|
\[
{}{y^{\prime }}^{2}-9 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.553 |
|
|
\[
{}{y^{\prime }}^{2} = x^{6}
\] |
[_quadrature] |
✓ |
0.464 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
1.190 |
|
|
\[
{}y^{\prime }+y = x^{2}+2 x -1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.056 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.846 |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
3.124 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.970 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
1.403 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }-\left (\ln \left (x \right )+1\right ) y = 0
\] |
[_separable] |
✓ |
1.560 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.423 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.444 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.197 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.168 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.124 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.054 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.078 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.036 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.015 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.483 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
1.151 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.260 |
|
|
\[
{}y^{\prime } = x -1
\] |
[_quadrature] |
✓ |
0.257 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
0.934 |
|
|
\[
{}y^{\prime } = y+1
\] |
[_quadrature] |
✓ |
0.919 |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
1.402 |
|
|
\[
{}y^{\prime } = 4-y^{2}
\] |
[_quadrature] |
✓ |
1.348 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
1.151 |
|
|
\[
{}y^{\prime } = -x y
\] |
[_separable] |
✓ |
1.402 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.024 |
|
|
\[
{}y^{\prime } = y^{2}-x^{2}
\] |
[_Riccati] |
✓ |
1.026 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.968 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
1.250 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
3.010 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.236 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.994 |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
1.462 |
|
|
\[
{}y^{\prime } = x^{3}+y^{3}
\] |
[_Abel] |
✗ |
0.665 |
|
|
\[
{}y^{\prime } = {| y|}
\] |
[_quadrature] |
✓ |
0.937 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.555 |
|
|
\[
{}y^{\prime } = \ln \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.306 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{3 y+x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.546 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.421 |
|
|
\[
{}y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x}
\] |
[_linear] |
✓ |
2.197 |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.875 |
|
|
\[
{}y^{\prime } = \frac {1}{x y}
\] |
[_separable] |
✓ |
1.405 |
|
|
\[
{}y^{\prime } = \ln \left (y-1\right )
\] |
[_quadrature] |
✓ |
0.902 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
30.253 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.888 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
2.120 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.885 |
|
|
\[
{}y^{\prime } = \frac {x y}{1-y}
\] |
[_separable] |
✓ |
1.147 |
|
|
\[
{}y^{\prime } = \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.680 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y-4}{x}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.368 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}+y^{{1}/{4}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
10.407 |
|
|
\[
{}y^{\prime } = 4 y-5
\] |
[_quadrature] |
✓ |
1.359 |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
1.344 |
|
|
\[
{}y^{\prime } = a y+b
\] |
[_quadrature] |
✓ |
0.875 |
|
|
\[
{}y^{\prime } = x^{2}+{\mathrm e}^{x}-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.665 |
|
|
\[
{}y^{\prime } = x y+\frac {1}{x^{2}+1}
\] |
[_linear] |
✓ |
2.084 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cos \left (x \right )
\] |
[_linear] |
✓ |
1.315 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (x \right )
\] |
[_linear] |
✓ |
2.115 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
2.991 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
2.844 |
|
|
\[
{}y^{\prime } = y \cot \left (x \right )+\csc \left (x \right )
\] |
[_linear] |
✓ |
1.799 |
|
|
\[
{}y^{\prime } = -x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
4.309 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.394 |
|
|
\[
{}y^{\prime } = 3 x +1
\] |
[_quadrature] |
✓ |
0.422 |
|
|
\[
{}y^{\prime } = x +\frac {1}{x}
\] |
[_quadrature] |
✓ |
0.517 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.530 |
|
|
\[
{}y^{\prime } = x \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.599 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.542 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.407 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.429 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.586 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.888 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.472 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
1.411 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.044 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.180 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y-x^{2}}
\] |
[_separable] |
✓ |
1.888 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.523 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y}
\] |
[_separable] |
✓ |
5.006 |
|
|
\[
{}y^{\prime } = -2 y+y^{2}
\] |
[_quadrature] |
✓ |
1.939 |
|
|
\[
{}y^{\prime } = x y+x
\] |
[_separable] |
✓ |
1.461 |
|
|
\[
{}x \,{\mathrm e}^{y}+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.351 |
|
|
\[
{}y-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.763 |
|
|
\[
{}2 y^{\prime } y = 1
\] |
[_quadrature] |
✓ |
1.321 |
|
|
\[
{}2 x y y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
1.929 |
|
|
\[
{}y^{\prime } = \frac {1-x y}{x^{2}}
\] |
[_linear] |
✓ |
0.960 |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.332 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{1-x y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.335 |
|
|
\[
{}y^{\prime } = 4 y+1
\] |
[_quadrature] |
✓ |
1.292 |
|
|
\[
{}y^{\prime } = x y+2
\] |
[_linear] |
✓ |
1.164 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.486 |
|