|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x x^{\prime } = 1-x t
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.421 |
|
|
\[
{}{x^{\prime }}^{2}+x t = \sqrt {1+t}
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.705 |
|
|
\[
{}x^{\prime } = -\frac {2 x}{t}+t
\] |
[_linear] |
✓ |
1.185 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.895 |
|
|
\[
{}x^{\prime }+2 x t = {\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.234 |
|
|
\[
{}t x^{\prime } = -x+t^{2}
\] |
[_linear] |
✓ |
1.093 |
|
|
\[
{}\theta ^{\prime } = -a \theta +{\mathrm e}^{b t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.853 |
|
|
\[
{}\left (t^{2}+1\right ) x^{\prime } = -3 x t +6 t
\] |
[_separable] |
✓ |
1.167 |
|
|
\[
{}x^{\prime }+\frac {5 x}{t} = 1+t
\] |
[_linear] |
✓ |
1.345 |
|
|
\[
{}x^{\prime } = \left (a +\frac {b}{t}\right ) x
\] |
[_separable] |
✓ |
1.070 |
|
|
\[
{}R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1}
\] |
[_linear] |
✓ |
1.562 |
|
|
\[
{}N^{\prime } = N-9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.936 |
|
|
\[
{}\cos \left (\theta \right ) v^{\prime }+v = 3
\] |
[_separable] |
✓ |
2.091 |
|
|
\[
{}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.224 |
|
|
\[
{}y^{\prime }+a y = \sqrt {1+t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.159 |
|
|
\[
{}x^{\prime } = 2 x t
\] |
[_separable] |
✓ |
0.990 |
|
|
\[
{}x^{\prime }+\frac {{\mathrm e}^{-t} x}{t} = t
\] |
[_linear] |
✓ |
1.815 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 3 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.329 |
|
|
\[
{}x^{\prime } = \left (t +x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.345 |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
0.302 |
|
|
\[
{}x^{\prime }+p \left (t \right ) x = 0
\] |
[_separable] |
✓ |
1.016 |
|
|
\[
{}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.509 |
|
|
\[
{}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right )
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.237 |
|
|
\[
{}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}}
\] |
[_separable] |
✓ |
2.362 |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.380 |
|
|
\[
{}x^{\prime } = a x+b x^{3}
\] |
[_quadrature] |
✓ |
0.952 |
|
|
\[
{}w^{\prime } = t w+t^{3} w^{3}
\] |
[_Bernoulli] |
✓ |
1.069 |
|
|
\[
{}x^{3}+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
1.490 |
|
|
\[
{}t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime } = 0
\] |
[_exact] |
✓ |
1.375 |
|
|
\[
{}x^{\prime } = -\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )}
\] |
[NONE] |
✓ |
52.672 |
|
|
\[
{}x+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
1.315 |
|
|
\[
{}x^{2}-t^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
1.921 |
|
|
\[
{}t \cot \left (x\right ) x^{\prime } = -2
\] |
[_separable] |
✓ |
1.842 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.032 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.272 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.047 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.954 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.019 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.568 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.040 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.984 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.160 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.056 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.920 |
|
|
\[
{}x^{\prime \prime }-12 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.461 |
|
|
\[
{}2 x^{\prime \prime }+3 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.135 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.980 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.068 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.260 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
24.111 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.536 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 12
\] |
[[_2nd_order, _missing_x]] |
✓ |
8.759 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
22.319 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
34.721 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
79.277 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
85.606 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = \left (t +2\right ) \sin \left (\pi t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
87.624 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
26.360 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.691 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.141 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.912 |
|
|
\[
{}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.990 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.408 |
|
|
\[
{}x^{\prime \prime }+x = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.691 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.825 |
|
|
\[
{}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.706 |
|
|
\[
{}x^{\prime \prime }-4 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.845 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.083 |
|
|
\[
{}x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.569 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.065 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.635 |
|
|
\[
{}x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.515 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
44.058 |
|
|
\[
{}x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.739 |
|
|
\[
{}x^{\prime \prime }+3025 x = \cos \left (45 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.092 |
|
|
\[
{}x^{\prime \prime } = -\frac {x}{t^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
1.736 |
|
|
\[
{}x^{\prime \prime } = \frac {4 x}{t^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.832 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.073 |
|
|
\[
{}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.012 |
|
|
\[
{}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.964 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.178 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.956 |
|
|
\[
{}t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.402 |
|
|
\[
{}x^{\prime \prime }+t^{2} x^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.856 |
|
|
\[
{}x^{\prime \prime }+x = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.701 |
|
|
\[
{}x^{\prime \prime }-x = t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.003 |
|
|
\[
{}x^{\prime \prime }-x = \frac {1}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.987 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 x = t^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.961 |
|
|
\[
{}x^{\prime \prime }+x = \frac {1}{1+t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.051 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.994 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{t} = a
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.958 |
|
|
\[
{}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.508 |
|
|
\[
{}x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.060 |
|
|
\[
{}x^{\prime \prime }+t x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.321 |
|
|
\[
{}x^{\prime \prime }-t x^{\prime }+x = 0
\] |
[_Hermite] |
✓ |
0.325 |
|
|
\[
{}x^{\prime \prime }-2 a x^{\prime }+a^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.312 |
|
|
\[
{}x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.306 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.356 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.057 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.086 |
|