|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right )
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.444 |
|
|
\[
{}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}}
\] |
[_separable] |
✓ |
3.677 |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.977 |
|
|
\[
{}x^{\prime } = a x+b x^{3}
\] |
[_quadrature] |
✓ |
1.684 |
|
|
\[
{}w^{\prime } = t w+t^{3} w^{3}
\] |
[_Bernoulli] |
✓ |
1.242 |
|
|
\[
{}x^{3}+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
2.240 |
|
|
\[
{}t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime } = 0
\] |
[_exact] |
✓ |
1.434 |
|
|
\[
{}x^{\prime } = -\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )}
\] |
[NONE] |
✓ |
20.473 |
|
|
\[
{}x+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
1.876 |
|
|
\[
{}x^{2}-t^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
2.856 |
|
|
\[
{}t \cot \left (x\right ) x^{\prime } = -2
\] |
[_separable] |
✓ |
2.324 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.521 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.333 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.494 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.664 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.489 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.385 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.497 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.655 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.222 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.994 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.363 |
|
|
\[
{}x^{\prime \prime }-12 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.167 |
|
|
\[
{}2 x^{\prime \prime }+3 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.066 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.664 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.194 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.296 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.086 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.164 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 12
\] |
[[_2nd_order, _missing_x]] |
✓ |
20.572 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.250 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.707 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.007 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
81.759 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = \left (t +2\right ) \sin \left (\pi t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
82.401 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
25.013 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
82.457 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
79.826 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.089 |
|
|
\[
{}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.741 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.217 |
|
|
\[
{}x^{\prime \prime }+x = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.252 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.802 |
|
|
\[
{}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.220 |
|
|
\[
{}x^{\prime \prime }-4 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.714 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.321 |
|
|
\[
{}x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
85.521 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.983 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.658 |
|
|
\[
{}x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.638 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.806 |
|
|
\[
{}x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.399 |
|
|
\[
{}x^{\prime \prime }+3025 x = \cos \left (45 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.711 |
|
|
\[
{}x^{\prime \prime } = -\frac {x}{t^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
1.152 |
|
|
\[
{}x^{\prime \prime } = \frac {4 x}{t^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
1.107 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.309 |
|
|
\[
{}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.130 |
|
|
\[
{}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.092 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.456 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.091 |
|
|
\[
{}t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.468 |
|
|
\[
{}x^{\prime \prime }+t^{2} x^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.900 |
|
|
\[
{}x^{\prime \prime }+x = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.161 |
|
|
\[
{}x^{\prime \prime }-x = t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.465 |
|
|
\[
{}x^{\prime \prime }-x = \frac {1}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.338 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 x = t^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.015 |
|
|
\[
{}x^{\prime \prime }+x = \frac {1}{1+t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.446 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.456 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{t} = a
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.056 |
|
|
\[
{}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.725 |
|
|
\[
{}x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.597 |
|
|
\[
{}x^{\prime \prime }+t x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.334 |
|
|
\[
{}x^{\prime \prime }-t x^{\prime }+x = 0
\] |
[_Hermite] |
✓ |
0.333 |
|
|
\[
{}x^{\prime \prime }-2 a x^{\prime }+a^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.330 |
|
|
\[
{}x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.318 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.366 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.094 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}x^{\prime \prime \prime }-x^{\prime }-8 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.115 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime } = 2 \,{\mathrm e}^{t}+3 t^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.129 |
|
|
\[
{}x^{\prime \prime \prime }-8 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.311 |
|
|
\[
{}x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.573 |
|
|
\[
{}x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.530 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }-6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.254 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.276 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.382 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.212 |
|
|
\[
{}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.179 |
|
|
\[
{}x^{\prime \prime }+9 x = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.339 |
|
|
\[
{}x^{\prime \prime }-2 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.298 |
|
|
\[
{}x^{\prime } = 2 x+\operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.482 |
|
|
\[
{}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.629 |
|
|
\[
{}x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.597 |
|
|
\[
{}x^{\prime } = -x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.598 |
|
|
\[
{}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (-t +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.683 |
|
|
\[
{}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.600 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.260 |
|
|
\[
{}x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (t -4\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.616 |
|