|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.541 |
|
|
\[
{}2 y x -\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.888 |
|
|
\[
{}1+y \,{\mathrm e}^{x}+x \,{\mathrm e}^{x} y+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.482 |
|
|
\[
{}\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }+\sin \left (y\right )-\sin \left (x \right ) y = 0
\] |
[_exact] |
✓ |
50.733 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.294 |
|
|
\[
{}{\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.955 |
|
|
\[
{}V^{\prime }\left (x \right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
0.527 |
|
|
\[
{}\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b = 0
\] |
[_separable] |
✓ |
1.334 |
|
|
\[
{}y x +y^{2}+x^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.904 |
|
|
\[
{}x^{\prime } = \frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{x t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
33.301 |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
0.753 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.941 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.007 |
|
|
\[
{}z^{\prime \prime }-4 z^{\prime }+13 z = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.910 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.936 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.286 |
|
|
\[
{}\theta ^{\prime \prime }+4 \theta = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.337 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.863 |
|
|
\[
{}2 z^{\prime \prime }+7 z^{\prime }-4 z = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.976 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.999 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+10 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.514 |
|
|
\[
{}4 x^{\prime \prime }-20 x^{\prime }+21 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.974 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.932 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.106 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.026 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.681 |
|
|
\[
{}x^{\prime \prime }-4 x = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.046 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.477 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.935 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.932 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.940 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.544 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \sin \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.037 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.784 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.076 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.006 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.944 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.041 |
|
|
\[
{}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.126 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \cos \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.743 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.140 |
|
|
\[
{}x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.126 |
|
|
\[
{}x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.113 |
|
|
\[
{}t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.318 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.318 |
|
|
\[
{}\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.485 |
|
|
\[
{}\left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.331 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Hermite] |
✓ |
0.322 |
|
|
\[
{}\tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.383 |
|
|
\[
{}x^{\prime \prime }-x = \frac {1}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.984 |
|
|
\[
{}y^{\prime \prime }+4 y = \cot \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.457 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 x = t^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.968 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.412 |
|
|
\[
{}\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.524 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.801 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.877 |
|
|
\[
{}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.665 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.535 |
|
|
\[
{}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.482 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.718 |
|
|
\[
{}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.324 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.801 |
|
|
\[
{}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.730 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.639 |
|
|
\[
{}a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.605 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.692 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Hermite] |
✓ |
0.446 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.547 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.765 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.476 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.496 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.175 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.585 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.102 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.766 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-y \\ y^{\prime }=2 x+y+t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.576 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y+\cos \left (2 t \right ) \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.783 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.586 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y+{\mathrm e}^{3 t} \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.534 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+5 y \\ y^{\prime }=-2 x+\cos \left (3 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.940 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{-t} \\ y^{\prime }=4 x-2 y+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.613 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.468 |
|
|
\(\left [\begin {array}{cc} 2 & 2 \\ 0 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.138 |
|
|
\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.189 |
|
|
\(\left [\begin {array}{cc} 9 & 2 \\ 2 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.138 |
|
|
\(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.104 |
|
|
\(\left [\begin {array}{cc} 2 & -3 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.178 |
|
|
\(\left [\begin {array}{cc} 6 & 0 \\ 0 & -13 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.128 |
|
|
\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.173 |
|
|
\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.099 |
|
|
\(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.176 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.309 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=-5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.279 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=11 x-2 y \\ y^{\prime }=3 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.305 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+20 y \\ y^{\prime }=40 x-19 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+2 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.276 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.566 |
|