|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )-x^{2} y^{2}
\] |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
0.152 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.704 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.531 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x = 2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.367 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.592 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 y^{\prime } x +6 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.182 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.416 |
|
|
\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.504 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.799 |
|
|
\[
{}x \left (x +2 y\right ) y^{\prime \prime }+2 x {y^{\prime }}^{2}+4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.844 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
3.829 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.539 |
|
|
\[
{}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.224 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.360 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+3 x+2 y={\mathrm e}^{t} \\ 4 x-3 y^{\prime }+3 y=3 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.514 |
|
|
\[
{}x^{\prime } = \frac {2 x}{t}
\] |
[_separable] |
✓ |
2.189 |
|
|
\[
{}x^{\prime } = -\frac {t}{x}
\] |
[_separable] |
✓ |
3.415 |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
1.268 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.142 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
1.247 |
|
|
\[
{}x^{\prime }+2 x = t^{2}+4 t +7
\] |
[[_linear, ‘class A‘]] |
✓ |
1.276 |
|
|
\[
{}2 t x^{\prime } = x
\] |
[_separable] |
✓ |
2.224 |
|
|
\[
{}t^{2} x^{\prime \prime }-6 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.655 |
|
|
\[
{}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.091 |
|
|
\[
{}x^{\prime } = x \left (1-\frac {x}{4}\right )
\] |
[_quadrature] |
✓ |
1.651 |
|
|
\[
{}x^{\prime } = x^{2}+t^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.028 |
|
|
\[
{}x^{\prime } = t \cos \left (t^{2}\right )
\] |
[_quadrature] |
✓ |
0.835 |
|
|
\[
{}x^{\prime } = \frac {1+t}{\sqrt {t}}
\] |
[_quadrature] |
✓ |
0.603 |
|
|
\[
{}x^{\prime \prime } = -3 \sqrt {t}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.946 |
|
|
\[
{}x^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
[_quadrature] |
✓ |
0.517 |
|
|
\[
{}x^{\prime } = \frac {1}{t \ln \left (t \right )}
\] |
[_quadrature] |
✓ |
0.428 |
|
|
\[
{}\sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right )
\] |
[_quadrature] |
✓ |
0.584 |
|
|
\[
{}x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}}
\] |
[_quadrature] |
✓ |
0.546 |
|
|
\[
{}x^{\prime }+t x^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.481 |
|
|
\[
{}x^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
1.112 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-2 x}
\] |
[_quadrature] |
✓ |
1.657 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.184 |
|
|
\[
{}u^{\prime } = \frac {1}{5-2 u}
\] |
[_quadrature] |
✓ |
1.163 |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
0.691 |
|
|
\[
{}Q^{\prime } = \frac {Q}{4+Q^{2}}
\] |
[_quadrature] |
✓ |
1.758 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
1.148 |
|
|
\[
{}y^{\prime } = r \left (a -y\right )
\] |
[_quadrature] |
✓ |
0.641 |
|
|
\[
{}x^{\prime } = \frac {2 x}{1+t}
\] |
[_separable] |
✓ |
2.051 |
|
|
\[
{}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right )
\] |
[_separable] |
✓ |
1.901 |
|
|
\[
{}\left (2 u+1\right ) u^{\prime }-1-t = 0
\] |
[_separable] |
✓ |
2.811 |
|
|
\[
{}R^{\prime } = \left (1+t \right ) \left (1+R^{2}\right )
\] |
[_separable] |
✓ |
2.295 |
|
|
\[
{}y^{\prime }+y+\frac {1}{y} = 0
\] |
[_quadrature] |
✓ |
13.081 |
|
|
\[
{}\left (1+t \right ) x^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
1.439 |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
[_quadrature] |
✓ |
1.654 |
|
|
\[
{}x^{\prime } = \left (4 t -x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.285 |
|
|
\[
{}x^{\prime } = 2 t x^{2}
\] |
[_separable] |
✓ |
2.464 |
|
|
\[
{}x^{\prime } = t^{2} {\mathrm e}^{-x}
\] |
[_separable] |
✓ |
3.393 |
|
|
\[
{}x^{\prime } = x \left (4+x\right )
\] |
[_quadrature] |
✓ |
2.257 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{t +x}
\] |
[_separable] |
✓ |
3.324 |
|
|
\[
{}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right )
\] |
[_separable] |
✓ |
1.950 |
|
|
\[
{}y^{\prime } = t^{2} \tan \left (y\right )
\] |
[_separable] |
✓ |
1.826 |
|
|
\[
{}x^{\prime } = \frac {\left (4+2 t \right ) x}{\ln \left (x\right )}
\] |
[_separable] |
✓ |
2.684 |
|
|
\[
{}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1}
\] |
[_separable] |
✓ |
2.166 |
|
|
\[
{}x^{\prime } = \frac {t^{2}}{1-x^{2}}
\] |
[_separable] |
✓ |
2.994 |
|
|
\[
{}x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
1.525 |
|
|
\[
{}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.199 |
|
|
\[
{}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.752 |
|
|
\[
{}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.064 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.693 |
|
|
\[
{}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}}
\] |
[_separable] |
✓ |
2.144 |
|
|
\[
{}x^{\prime } = 2 t^{3} x-6
\] |
[_linear] |
✓ |
1.724 |
|
|
\[
{}\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right ) = 0
\] |
[_separable] |
✓ |
2.444 |
|
|
\[
{}x^{\prime } = t -x^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.987 |
|
|
\[
{}7 t^{2} x^{\prime } = 3 x-2 t
\] |
[_linear] |
✓ |
1.218 |
|
|
\[
{}x x^{\prime } = 1-t x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.714 |
|
|
\[
{}{x^{\prime }}^{2}+t x = \sqrt {1+t}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.661 |
|
|
\[
{}x^{\prime } = -\frac {2 x}{t}+t
\] |
[_linear] |
✓ |
1.675 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.222 |
|
|
\[
{}x^{\prime }+2 t x = {\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.576 |
|
|
\[
{}t x^{\prime } = -x+t^{2}
\] |
[_linear] |
✓ |
1.544 |
|
|
\[
{}\theta ^{\prime } = -a \theta +{\mathrm e}^{b t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.902 |
|
|
\[
{}\left (t^{2}+1\right ) x^{\prime } = -3 t x+6 t
\] |
[_separable] |
✓ |
1.604 |
|
|
\[
{}x^{\prime }+\frac {5 x}{t} = 1+t
\] |
[_linear] |
✓ |
1.860 |
|
|
\[
{}x^{\prime } = \left (a +\frac {b}{t}\right ) x
\] |
[_separable] |
✓ |
1.035 |
|
|
\[
{}R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1}
\] |
[_linear] |
✓ |
2.435 |
|
|
\[
{}N^{\prime } = N-9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.330 |
|
|
\[
{}\cos \left (\theta \right ) v^{\prime }+v = 3
\] |
[_separable] |
✓ |
2.483 |
|
|
\[
{}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.722 |
|
|
\[
{}y^{\prime }+a y = \sqrt {1+t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.179 |
|
|
\[
{}x^{\prime } = 2 t x
\] |
[_separable] |
✓ |
1.580 |
|
|
\[
{}x^{\prime }+\frac {{\mathrm e}^{-t} x}{t} = t
\] |
[_linear] |
✓ |
2.036 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 3 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.117 |
|
|
\[
{}x^{\prime } = \left (t +x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.705 |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
0.698 |
|
|
\[
{}x^{\prime }+p \left (t \right ) x = 0
\] |
[_separable] |
✓ |
0.908 |
|
|
\[
{}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.264 |
|
|
\[
{}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right )
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.332 |
|
|
\[
{}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}}
\] |
[_separable] |
✓ |
2.957 |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.909 |
|
|
\[
{}x^{\prime } = a x+b x^{3}
\] |
[_quadrature] |
✓ |
1.484 |
|
|
\[
{}w^{\prime } = t w+t^{3} w^{3}
\] |
[_Bernoulli] |
✓ |
1.227 |
|
|
\[
{}x^{3}+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
2.533 |
|
|
\[
{}t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime } = 0
\] |
[_exact] |
✓ |
1.428 |
|
|
\[
{}x^{\prime } = -\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )}
\] |
[NONE] |
✓ |
28.971 |
|
|
\[
{}x+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
2.003 |
|