|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.310 |
|
|
\[
{}y^{\prime } = \frac {x y}{1-y}
\] |
[_separable] |
✓ |
1.406 |
|
|
\[
{}y^{\prime } = \left (x y\right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.214 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y-4}{x}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
6.358 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}+y^{{1}/{4}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
16.587 |
|
|
\[
{}y^{\prime } = 4 y-5
\] |
[_quadrature] |
✓ |
2.080 |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
2.175 |
|
|
\[
{}y^{\prime } = a y+b
\] |
[_quadrature] |
✓ |
1.047 |
|
|
\[
{}y^{\prime } = x^{2}+{\mathrm e}^{x}-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.905 |
|
|
\[
{}y^{\prime } = x y+\frac {1}{x^{2}+1}
\] |
[_linear] |
✓ |
2.220 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cos \left (x \right )
\] |
[_linear] |
✓ |
1.778 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (x \right )
\] |
[_linear] |
✓ |
2.036 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
2.713 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+4}+\sqrt {x}
\] |
[_linear] |
✓ |
2.571 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) y+\csc \left (x \right )
\] |
[_linear] |
✓ |
2.009 |
|
|
\[
{}y^{\prime } = -x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
6.395 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.348 |
|
|
\[
{}y^{\prime } = 3 x +1
\] |
[_quadrature] |
✓ |
0.674 |
|
|
\[
{}y^{\prime } = x +\frac {1}{x}
\] |
[_quadrature] |
✓ |
0.743 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.749 |
|
|
\[
{}y^{\prime } = x \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.796 |
|
|
\[
{}y^{\prime } = \frac {1}{-1+x}
\] |
[_quadrature] |
✓ |
0.730 |
|
|
\[
{}y^{\prime } = \frac {1}{-1+x}
\] |
[_quadrature] |
✓ |
0.634 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.674 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.744 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
1.121 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.710 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
3.223 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.314 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.795 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y-x^{2}}
\] |
[_separable] |
✓ |
2.316 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
2.039 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y}
\] |
[_separable] |
✓ |
8.974 |
|
|
\[
{}y^{\prime } = -2 y+y^{2}
\] |
[_quadrature] |
✓ |
2.740 |
|
|
\[
{}y^{\prime } = x y+x
\] |
[_separable] |
✓ |
1.961 |
|
|
\[
{}x \,{\mathrm e}^{y}+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.711 |
|
|
\[
{}y-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.751 |
|
|
\[
{}2 y y^{\prime } = 1
\] |
[_quadrature] |
✓ |
1.887 |
|
|
\[
{}2 x y y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.777 |
|
|
\[
{}y^{\prime } = \frac {1-x y}{x^{2}}
\] |
[_linear] |
✓ |
1.252 |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x +y\right )}{x \left (x +2 y\right )}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
62.497 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{1-x y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.636 |
|
|
\[
{}y^{\prime } = 4 y+1
\] |
[_quadrature] |
✓ |
2.049 |
|
|
\[
{}y^{\prime } = x y+2
\] |
[_linear] |
✓ |
1.462 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
2.019 |
|
|
\[
{}y^{\prime } = \frac {y}{-1+x}+x^{2}
\] |
[_linear] |
✓ |
1.425 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right )
\] |
[_linear] |
✓ |
2.204 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x}
\] |
[_linear] |
✓ |
2.205 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) y+\sin \left (x \right )
\] |
[_linear] |
✓ |
2.153 |
|
|
\[
{}x -y y^{\prime } = 0
\] |
[_separable] |
✓ |
4.461 |
|
|
\[
{}y-x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.659 |
|
|
\[
{}x^{2}-y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.601 |
|
|
\[
{}x y \left (1-y\right )-2 y^{\prime } = 0
\] |
[_separable] |
✓ |
2.507 |
|
|
\[
{}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.506 |
|
|
\[
{}y \left (2 x -1\right )+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.705 |
|
|
\[
{}y^{\prime } = \frac {1}{-1+x}
\] |
[_quadrature] |
✓ |
0.615 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.505 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
2.021 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
2.007 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.208 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
1.783 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.247 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.297 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.937 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.214 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
3.354 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
4.831 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
10.761 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.052 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.897 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.560 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.117 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.194 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.040 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.329 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.958 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
40.444 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
8.617 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
114.345 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
11.530 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
14.012 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
19.111 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
3.829 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
61.680 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.569 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.072 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.919 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.243 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.011 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.389 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.907 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
4.109 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
84.826 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
7.483 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
3.225 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.750 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.522 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.593 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
3.022 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.497 |
|