|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.428 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.913 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.102 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.466 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.901 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 12
\] |
[[_2nd_order, _missing_x]] |
✓ |
37.810 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.170 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.533 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.485 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
80.365 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = \left (t +2\right ) \sin \left (\pi t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
82.543 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
24.681 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
80.782 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.950 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.796 |
|
|
\[
{}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.604 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.566 |
|
|
\[
{}x^{\prime \prime }+x = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.030 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.613 |
|
|
\[
{}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.979 |
|
|
\[
{}x^{\prime \prime }-4 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.466 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.629 |
|
|
\[
{}x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.830 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.741 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime } = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.800 |
|
|
\[
{}x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.508 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.090 |
|
|
\[
{}x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.422 |
|
|
\[
{}x^{\prime \prime }+3025 x = \cos \left (45 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.922 |
|
|
\[
{}x^{\prime \prime } = -\frac {x}{t^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
1.072 |
|
|
\[
{}x^{\prime \prime } = \frac {4 x}{t^{2}}
\] |
[[_Emden, _Fowler]] |
✓ |
1.132 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 x^{\prime } t +x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.356 |
|
|
\[
{}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.190 |
|
|
\[
{}t^{2} x^{\prime \prime }-7 x^{\prime } t +16 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.170 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 x^{\prime } t -8 x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.638 |
|
|
\[
{}t^{2} x^{\prime \prime }+x^{\prime } t = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.147 |
|
|
\[
{}t^{2} x^{\prime \prime }-x^{\prime } t +2 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.566 |
|
|
\[
{}x^{\prime \prime }+t^{2} x^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.049 |
|
|
\[
{}x^{\prime \prime }+x = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.062 |
|
|
\[
{}x^{\prime \prime }-x = t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.146 |
|
|
\[
{}x^{\prime \prime }-x = \frac {1}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.139 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 x = t^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.993 |
|
|
\[
{}x^{\prime \prime }+x = \frac {1}{t +1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.176 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.187 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{t} = a
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.117 |
|
|
\[
{}t^{2} x^{\prime \prime }-3 x^{\prime } t +3 x = 4 t^{7}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.796 |
|
|
\[
{}x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{{\mathrm e}^{t}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.422 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } t +x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.351 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } t +x = 0
\] |
[_Hermite] |
✓ |
0.345 |
|
|
\[
{}x^{\prime \prime }-2 a x^{\prime }+a^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.341 |
|
|
\[
{}x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}t^{2} x^{\prime \prime }+x^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.383 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.097 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}x^{\prime \prime \prime }-x^{\prime }-8 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.115 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime } = 2 \,{\mathrm e}^{t}+3 t^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.135 |
|
|
\[
{}x^{\prime \prime \prime }-8 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.590 |
|
|
\[
{}x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.443 |
|
|
\[
{}x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.393 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }-6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.279 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.300 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.338 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.204 |
|
|
\[
{}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.349 |
|
|
\[
{}x^{\prime \prime }+9 x = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.352 |
|
|
\[
{}x^{\prime \prime }-2 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.298 |
|
|
\[
{}x^{\prime } = 2 x+\operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.389 |
|
|
\[
{}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.661 |
|
|
\[
{}x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.437 |
|
|
\[
{}x^{\prime } = -x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.563 |
|
|
\[
{}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (-t +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.707 |
|
|
\[
{}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.628 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.315 |
|
|
\[
{}x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (-4+t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.597 |
|
|
\[
{}x^{\prime \prime }-x = \delta \left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.336 |
|
|
\[
{}x^{\prime \prime }+x = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.345 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.207 |
|
|
\[
{}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.513 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.641 |
|
|
\[
{}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.061 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.413 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.264 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.273 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.297 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.354 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.379 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.559 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.374 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.297 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.316 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.333 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 y \\ y^{\prime }=6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.289 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=-x-14 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.035 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 y-3 x \\ y^{\prime }=x+2 y-1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.826 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|