|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y = 0
\] |
[_separable] |
✓ |
1.447 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.930 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.974 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.772 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.776 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.798 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.810 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.904 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.827 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.276 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
1.026 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.214 |
|
|
\[
{}y^{\prime } = x -1
\] |
[_quadrature] |
✓ |
0.216 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
0.341 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
0.299 |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
0.468 |
|
|
\[
{}y^{\prime } = 4-y^{2}
\] |
[_quadrature] |
✓ |
0.576 |
|
|
\[
{}y^{\prime } = y x
\] |
[_separable] |
✓ |
0.977 |
|
|
\[
{}y^{\prime } = -y x
\] |
[_separable] |
✓ |
1.205 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
0.978 |
|
|
\[
{}y^{\prime } = y^{2}-x^{2}
\] |
[_Riccati] |
✓ |
0.979 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.813 |
|
|
\[
{}y^{\prime } = y x
\] |
[_separable] |
✓ |
0.978 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
2.580 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.068 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.393 |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
0.655 |
|
|
\[
{}y^{\prime } = x^{3}+y^{3}
\] |
[_Abel] |
✗ |
0.288 |
|
|
\[
{}y^{\prime } = {| y|}
\] |
[_quadrature] |
✓ |
0.870 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.328 |
|
|
\[
{}y^{\prime } = \ln \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.110 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.312 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.917 |
|
|
\[
{}y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x}
\] |
[_linear] |
✓ |
2.083 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.605 |
|
|
\[
{}y^{\prime } = \frac {1}{y x}
\] |
[_separable] |
✓ |
1.182 |
|
|
\[
{}y^{\prime } = \ln \left (-1+y\right )
\] |
[_quadrature] |
✓ |
0.344 |
|
|
\[
{}y^{\prime } = \sqrt {\left (2+y\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
28.177 |
|
|
\[
{}y^{\prime } = \frac {y}{-x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.286 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
1.912 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.460 |
|
|
\[
{}y^{\prime } = \frac {x y}{1-y}
\] |
[_separable] |
✓ |
1.022 |
|
|
\[
{}y^{\prime } = \left (y x \right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.360 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y-4}{x}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.967 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}+y^{{1}/{4}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.698 |
|
|
\[
{}y^{\prime } = 4 y-5
\] |
[_quadrature] |
✓ |
0.638 |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
0.632 |
|
|
\[
{}y^{\prime } = a y+b
\] |
[_quadrature] |
✓ |
0.455 |
|
|
\[
{}y^{\prime } = x^{2}+{\mathrm e}^{x}-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.542 |
|
|
\[
{}y^{\prime } = y x +\frac {1}{x^{2}+1}
\] |
[_linear] |
✓ |
1.854 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cos \left (x \right )
\] |
[_linear] |
✓ |
1.178 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (x \right )
\] |
[_linear] |
✓ |
1.950 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
2.839 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
2.703 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) y+\csc \left (x \right )
\] |
[_linear] |
✓ |
1.473 |
|
|
\[
{}y^{\prime } = -x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
3.986 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.187 |
|
|
\[
{}y^{\prime } = 3 x +1
\] |
[_quadrature] |
✓ |
0.333 |
|
|
\[
{}y^{\prime } = x +\frac {1}{x}
\] |
[_quadrature] |
✓ |
0.399 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.411 |
|
|
\[
{}y^{\prime } = x \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.440 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.394 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.333 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.366 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.406 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.730 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.408 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
0.791 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
0.394 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
0.440 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y-x^{2}}
\] |
[_separable] |
✓ |
1.637 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.314 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y}
\] |
[_separable] |
✓ |
5.077 |
|
|
\[
{}y^{\prime } = -2 y+y^{2}
\] |
[_quadrature] |
✓ |
1.019 |
|
|
\[
{}y^{\prime } = y x +x
\] |
[_separable] |
✓ |
1.247 |
|
|
\[
{}x \,{\mathrm e}^{y}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.573 |
|
|
\[
{}y-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.674 |
|
|
\[
{}2 y y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.462 |
|
|
\[
{}2 x y y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
1.677 |
|
|
\[
{}y^{\prime } = \frac {1-y x}{x^{2}}
\] |
[_linear] |
✓ |
0.879 |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.102 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{1-y x}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.205 |
|
|
\[
{}y^{\prime } = 4 y+1
\] |
[_quadrature] |
✓ |
0.605 |
|
|
\[
{}y^{\prime } = y x +2
\] |
[_linear] |
✓ |
0.998 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.272 |
|
|
\[
{}y^{\prime } = \frac {y}{x -1}+x^{2}
\] |
[_linear] |
✓ |
0.971 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right )
\] |
[_linear] |
✓ |
1.605 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.590 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) y+\sin \left (x \right )
\] |
[_linear] |
✓ |
1.691 |
|
|
\[
{}x -y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.579 |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.067 |
|
|
\[
{}x^{2}-y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.062 |
|
|
\[
{}x y \left (1-y\right )-2 y^{\prime } = 0
\] |
[_separable] |
✓ |
1.818 |
|
|
\[
{}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.168 |
|
|
\[
{}y \left (2 x -1\right )+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.178 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.336 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.944 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.258 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.313 |
|