|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.328 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
1.993 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.452 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
0.483 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
0.655 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
0.547 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
0.708 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
0.562 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.775 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.025 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
1.767 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.957 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.236 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.098 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.225 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.182 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
20.920 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
6.994 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
11.797 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
5.860 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
12.427 |
|
|
\[
{}y^{\prime } = \sqrt {\left (2+y\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
3.176 |
|
|
\[
{}y^{\prime } = \sqrt {\left (2+y\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
5.454 |
|
|
\[
{}y^{\prime } = \sqrt {\left (2+y\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
20.622 |
|
|
\[
{}y^{\prime } = \frac {y}{-x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.676 |
|
|
\[
{}y^{\prime } = \frac {y}{-x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.025 |
|
|
\[
{}y^{\prime } = \frac {y}{-x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.979 |
|
|
\[
{}y^{\prime } = \frac {y}{-x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.951 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.813 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.724 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.760 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
3.908 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
4.482 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
3.070 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.956 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.419 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.158 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.512 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.604 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.101 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.402 |
|
|
\[
{}x y^{\prime \prime \prime }+y^{\prime } x = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.623 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.430 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.748 |
|
|
\[
{}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.374 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.223 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.757 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.658 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.911 |
|
|
\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.300 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.999 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.754 |
|
|
\[
{}y^{\prime \prime }-4 y = 31
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.503 |
|
|
\[
{}y^{\prime \prime }+9 y = 27 x +18
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.616 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = -3 x -\frac {3}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.497 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.730 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.117 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime \prime }+\alpha y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.456 |
|
|
\[
{}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime }-i y = 0
\] |
[_quadrature] |
✓ |
0.692 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.566 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3+\cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.160 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 x^{2} {\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.156 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.486 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.247 |
|
|
\[
{}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.240 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 x +4
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.260 |
|
|
\[
{}y^{\prime }+2 y = 4
\] |
[_quadrature] |
✓ |
0.168 |
|
|
\[
{}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.279 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.295 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.234 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.230 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.234 |
|
|
\[
{}y^{\prime \prime }-9 y = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.363 |
|
|
\[
{}y^{\prime \prime }+9 y = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.356 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.570 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.379 |
|
|
\[
{}y^{\prime }-2 y = 6
\] |
[_quadrature] |
✓ |
0.254 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.264 |
|
|
\[
{}y^{\prime \prime }+9 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|