|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{x^{\prime }}^{2}+t x = \sqrt {t +1}
\] |
[‘y=_G(x,y’)‘] |
✓ |
4.350 |
|
|
\[
{}x^{\prime } = -\frac {2 x}{t}+t
\] |
[_linear] |
✓ |
1.643 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.322 |
|
|
\[
{}x^{\prime }+2 t x = {\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.688 |
|
|
\[
{}t x^{\prime } = -x+t^{2}
\] |
[_linear] |
✓ |
1.467 |
|
|
\[
{}\theta ^{\prime } = -a \theta +{\mathrm e}^{t b}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.945 |
|
|
\[
{}\left (t^{2}+1\right ) x^{\prime } = -3 t x+6 t
\] |
[_separable] |
✓ |
2.030 |
|
|
\[
{}x^{\prime }+\frac {5 x}{t} = t +1
\] |
[_linear] |
✓ |
1.825 |
|
|
\[
{}x^{\prime } = \left (a +\frac {b}{t}\right ) x
\] |
[_separable] |
✓ |
1.299 |
|
|
\[
{}R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1}
\] |
[_linear] |
✓ |
1.971 |
|
|
\[
{}N^{\prime } = N-9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.379 |
|
|
\[
{}\cos \left (\theta \right ) v^{\prime }+v = 3
\] |
[_separable] |
✓ |
3.043 |
|
|
\[
{}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.818 |
|
|
\[
{}y^{\prime }+a y = \sqrt {t +1}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.312 |
|
|
\[
{}x^{\prime } = 2 t x
\] |
[_separable] |
✓ |
1.662 |
|
|
\[
{}x^{\prime }+\frac {{\mathrm e}^{-t} x}{t} = t
\] |
[_linear] |
✓ |
1.899 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 3 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.931 |
|
|
\[
{}x^{\prime } = \left (t +x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.538 |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
0.873 |
|
|
\[
{}x^{\prime }+p \left (t \right ) x = 0
\] |
[_separable] |
✓ |
0.757 |
|
|
\[
{}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.543 |
|
|
\[
{}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right )
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.740 |
|
|
\[
{}x^{\prime } = -\frac {x}{t}+\frac {1}{t x^{2}}
\] |
[_separable] |
✓ |
4.237 |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.337 |
|
|
\[
{}x^{\prime } = a x+b x^{3}
\] |
[_quadrature] |
✓ |
8.486 |
|
|
\[
{}w^{\prime } = t w+t^{3} w^{3}
\] |
[_Bernoulli] |
✓ |
1.484 |
|
|
\[
{}x^{3}+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
2.270 |
|
|
\[
{}t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime } = 0
\] |
[_exact] |
✓ |
1.539 |
|
|
\[
{}x^{\prime } = -\frac {\sin \left (x\right )-x \sin \left (t \right )}{t \cos \left (x\right )+\cos \left (t \right )}
\] |
[NONE] |
✓ |
27.822 |
|
|
\[
{}x+3 t x^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
2.211 |
|
|
\[
{}x^{2}-t^{2} x^{\prime } = 0
\] |
[_separable] |
✓ |
2.902 |
|
|
\[
{}t \cot \left (x\right ) x^{\prime } = -2
\] |
[_separable] |
✓ |
2.674 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.345 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.115 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.359 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.408 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.335 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.246 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.359 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.408 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.156 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.869 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.030 |
|
|
\[
{}x^{\prime \prime }-12 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.855 |
|
|
\[
{}2 x^{\prime \prime }+3 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.957 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.419 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.056 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.051 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
31.162 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
34.812 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 12
\] |
[[_2nd_order, _missing_x]] |
✓ |
15.719 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.881 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.008 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
80.613 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
83.910 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = \left (t +2\right ) \sin \left (\pi t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
84.049 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
36.348 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
82.109 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
80.829 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.533 |
|
|
\[
{}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.456 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.074 |
|
|
\[
{}x^{\prime \prime }+x = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.809 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.551 |
|
|
\[
{}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.887 |
|
|
\[
{}x^{\prime \prime }-4 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.436 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.516 |
|
|
\[
{}x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
81.078 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.658 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.503 |
|
|
\[
{}x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.201 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.291 |
|
|
\[
{}x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.277 |
|
|
\[
{}x^{\prime \prime }+3025 x = \cos \left (45 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
33.619 |
|
|
\[
{}x^{\prime \prime } = -\frac {x}{t^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
2.040 |
|
|
\[
{}x^{\prime \prime } = \frac {4 x}{t^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
0.727 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.071 |
|
|
\[
{}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.893 |
|
|
\[
{}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.875 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.114 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.841 |
|
|
\[
{}t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.301 |
|
|
\[
{}x^{\prime \prime }+t^{2} x^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.510 |
|
|
\[
{}x^{\prime \prime }+x = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.891 |
|
|
\[
{}x^{\prime \prime }-x = t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.207 |
|
|
\[
{}x^{\prime \prime }-x = \frac {1}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.161 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 x = t^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.850 |
|
|
\[
{}x^{\prime \prime }+x = \frac {1}{t +1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.319 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.276 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{t} = a
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.940 |
|
|
\[
{}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.588 |
|
|
\[
{}x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.337 |
|
|
\[
{}x^{\prime \prime }+t x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.105 |
|
|
\[
{}x^{\prime \prime }-t x^{\prime }+x = 0
\] |
[_Hermite] |
✓ |
0.108 |
|
|
\[
{}x^{\prime \prime }-2 a x^{\prime }+a^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.092 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.147 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.054 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.043 |
|