|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime } = \frac {2 x}{t}
\] |
[_separable] |
✓ |
1.596 |
|
|
\[
{}x^{\prime } = -\frac {t}{x}
\] |
[_separable] |
✓ |
2.819 |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
0.941 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.291 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.937 |
|
|
\[
{}x^{\prime }+2 x = t^{2}+4 t +7
\] |
[[_linear, ‘class A‘]] |
✓ |
1.085 |
|
|
\[
{}2 x^{\prime } t = x
\] |
[_separable] |
✓ |
1.673 |
|
|
\[
{}t^{2} x^{\prime \prime }-6 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.722 |
|
|
\[
{}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.854 |
|
|
\[
{}x^{\prime } = x \left (1-\frac {x}{4}\right )
\] |
[_quadrature] |
✓ |
1.649 |
|
|
\[
{}x^{\prime } = x^{2}+t^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.017 |
|
|
\[
{}x^{\prime } = t \cos \left (t^{2}\right )
\] |
[_quadrature] |
✓ |
0.655 |
|
|
\[
{}x^{\prime } = \frac {t +1}{\sqrt {t}}
\] |
[_quadrature] |
✓ |
0.577 |
|
|
\[
{}x^{\prime \prime } = -3 \sqrt {t}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.779 |
|
|
\[
{}x^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
[_quadrature] |
✓ |
0.336 |
|
|
\[
{}x^{\prime } = \frac {1}{t \ln \left (t \right )}
\] |
[_quadrature] |
✓ |
0.286 |
|
|
\[
{}\sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right )
\] |
[_quadrature] |
✓ |
0.431 |
|
|
\[
{}x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}}
\] |
[_quadrature] |
✓ |
0.642 |
|
|
\[
{}t x^{\prime \prime }+x^{\prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.545 |
|
|
\[
{}x^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
1.331 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-2 x}
\] |
[_quadrature] |
✓ |
1.374 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.016 |
|
|
\[
{}u^{\prime } = \frac {1}{5-2 u}
\] |
[_quadrature] |
✓ |
1.014 |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
0.778 |
|
|
\[
{}Q^{\prime } = \frac {Q}{4+Q^{2}}
\] |
[_quadrature] |
✓ |
1.496 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.951 |
|
|
\[
{}y^{\prime } = r \left (a -y\right )
\] |
[_quadrature] |
✓ |
0.709 |
|
|
\[
{}x^{\prime } = \frac {2 x}{t +1}
\] |
[_separable] |
✓ |
1.646 |
|
|
\[
{}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right )
\] |
[_separable] |
✓ |
1.820 |
|
|
\[
{}\left (2 u+1\right ) u^{\prime }-t -1 = 0
\] |
[_separable] |
✓ |
2.346 |
|
|
\[
{}R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right )
\] |
[_separable] |
✓ |
2.094 |
|
|
\[
{}y^{\prime }+y+\frac {1}{y} = 0
\] |
[_quadrature] |
✓ |
15.523 |
|
|
\[
{}\left (t +1\right ) x^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
1.158 |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
[_quadrature] |
✓ |
1.444 |
|
|
\[
{}x^{\prime } = \left (4 t -x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.341 |
|
|
\[
{}x^{\prime } = 2 t x^{2}
\] |
[_separable] |
✓ |
2.134 |
|
|
\[
{}x^{\prime } = t^{2} {\mathrm e}^{-x}
\] |
[_separable] |
✓ |
3.002 |
|
|
\[
{}x^{\prime } = x \left (4+x\right )
\] |
[_quadrature] |
✓ |
2.297 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{t +x}
\] |
[_separable] |
✓ |
3.328 |
|
|
\[
{}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right )
\] |
[_separable] |
✓ |
2.197 |
|
|
\[
{}y^{\prime } = t^{2} \tan \left (y\right )
\] |
[_separable] |
✓ |
1.858 |
|
|
\[
{}x^{\prime } = \frac {\left (4+2 t \right ) x}{\ln \left (x\right )}
\] |
[_separable] |
✓ |
2.700 |
|
|
\[
{}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1}
\] |
[_separable] |
✓ |
1.873 |
|
|
\[
{}x^{\prime } = \frac {t^{2}}{1-x^{2}}
\] |
[_separable] |
✓ |
3.042 |
|
|
\[
{}x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
3.256 |
|
|
\[
{}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 x t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.911 |
|
|
\[
{}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.619 |
|
|
\[
{}\frac {t x^{\prime \prime }+x^{\prime }}{t} = -2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.021 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.368 |
|
|
\[
{}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}}
\] |
[_separable] |
✓ |
1.863 |
|
|
\[
{}x^{\prime } = 2 t^{3} x-6
\] |
[_linear] |
✓ |
1.393 |
|
|
\[
{}\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right ) = 0
\] |
[_separable] |
✓ |
2.408 |
|
|
\[
{}x^{\prime } = t -x^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.961 |
|
|
\[
{}7 t^{2} x^{\prime } = 3 x-2 t
\] |
[_linear] |
✓ |
1.102 |
|
|
\[
{}x x^{\prime } = 1-x t
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.657 |
|
|
\[
{}{x^{\prime }}^{2}+x t = \sqrt {t +1}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.862 |
|
|
\[
{}x^{\prime } = -\frac {2 x}{t}+t
\] |
[_linear] |
✓ |
1.338 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.021 |
|
|
\[
{}x^{\prime }+2 x t = {\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.378 |
|
|
\[
{}x^{\prime } t = -x+t^{2}
\] |
[_linear] |
✓ |
1.273 |
|
|
\[
{}\theta ^{\prime } = -a \theta +{\mathrm e}^{t b}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.925 |
|
|
\[
{}\left (t^{2}+1\right ) x^{\prime } = -3 x t +6 t
\] |
[_separable] |
✓ |
1.313 |
|
|
\[
{}x^{\prime }+\frac {5 x}{t} = t +1
\] |
[_linear] |
✓ |
1.528 |
|
|
\[
{}x^{\prime } = \left (a +\frac {b}{t}\right ) x
\] |
[_separable] |
✓ |
1.142 |
|
|
\[
{}R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1}
\] |
[_linear] |
✓ |
1.711 |
|
|
\[
{}N^{\prime } = N-9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.083 |
|
|
\[
{}\cos \left (\theta \right ) v^{\prime }+v = 3
\] |
[_separable] |
✓ |
2.207 |
|
|
\[
{}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.452 |
|
|
\[
{}y^{\prime }+a y = \sqrt {t +1}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.255 |
|
|
\[
{}x^{\prime } = 2 x t
\] |
[_separable] |
✓ |
1.165 |
|
|
\[
{}x^{\prime }+\frac {{\mathrm e}^{-t} x}{t} = t
\] |
[_linear] |
✓ |
2.005 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 3 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.511 |
|
|
\[
{}x^{\prime } = \left (t +x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.499 |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
0.736 |
|
|
\[
{}x^{\prime }+p \left (t \right ) x = 0
\] |
[_separable] |
✓ |
1.139 |
|
|
\[
{}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.968 |
|
|
\[
{}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right )
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.348 |
|
|
\[
{}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}}
\] |
[_separable] |
✓ |
3.672 |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.587 |
|
|
\[
{}x^{\prime } = a x+b x^{3}
\] |
[_quadrature] |
✓ |
1.894 |
|
|
\[
{}w^{\prime } = t w+t^{3} w^{3}
\] |
[_Bernoulli] |
✓ |
1.221 |
|
|
\[
{}x^{3}+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
1.773 |
|
|
\[
{}t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime } = 0
\] |
[_exact] |
✓ |
1.520 |
|
|
\[
{}x^{\prime } = -\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )}
\] |
[NONE] |
✓ |
28.273 |
|
|
\[
{}x+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
1.533 |
|
|
\[
{}x^{2}-t^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
2.194 |
|
|
\[
{}t \cot \left (x\right ) x^{\prime } = -2
\] |
[_separable] |
✓ |
2.127 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.158 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.413 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.190 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.412 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.178 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.750 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.197 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.431 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.148 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.796 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.205 |
|
|
\[
{}x^{\prime \prime }-12 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.895 |
|
|
\[
{}2 x^{\prime \prime }+3 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.836 |
|