|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.117 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.121 |
|
|
\[
{}x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.156 |
|
|
\[
{}x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.105 |
|
|
\[
{}t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.098 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.101 |
|
|
\[
{}\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.306 |
|
|
\[
{}\left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[_Hermite] |
✓ |
0.103 |
|
|
\[
{}\tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.093 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.106 |
|
|
\[
{}x^{\prime \prime }-x = \frac {1}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.188 |
|
|
\[
{}y^{\prime \prime }+4 y = \cot \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.555 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 x = t^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.858 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.916 |
|
|
\[
{}\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.416 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.377 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.776 |
|
|
\[
{}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.034 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.573 |
|
|
\[
{}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.876 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.704 |
|
|
\[
{}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.580 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.867 |
|
|
\[
{}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.645 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
5.295 |
|
|
\[
{}a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
17.266 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.648 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[_Hermite] |
✓ |
0.309 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.365 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.704 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.342 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.331 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.280 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.426 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.123 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.647 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-y \\ y^{\prime }=2 x+y+t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.660 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y+\cos \left (2 t \right ) \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.880 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.646 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y+{\mathrm e}^{3 t} \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.583 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+5 y \\ y^{\prime }=-2 x+\cos \left (3 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.224 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{-t} \\ y^{\prime }=4 x-2 y+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.709 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.633 |
|
|
\(\left [\begin {array}{cc} 2 & 2 \\ 0 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.127 |
|
|
\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.237 |
|
|
\(\left [\begin {array}{cc} 9 & 2 \\ 2 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.128 |
|
|
\(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.090 |
|
|
\(\left [\begin {array}{cc} 2 & -3 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.151 |
|
|
\(\left [\begin {array}{cc} 6 & 0 \\ 0 & -13 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.109 |
|
|
\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.168 |
|
|
\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.084 |
|
|
\(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.124 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=-5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=11 x-2 y \\ y^{\prime }=3 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.467 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+20 y \\ y^{\prime }=40 x-19 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+2 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.768 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-6 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.552 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-11 x-2 y \\ y^{\prime }=13 x-9 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-5 y \\ y^{\prime }=10 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.566 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.446 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=13 x \\ y^{\prime }=13 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.293 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.435 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.318 |
|
|
\[
{}\tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.064 |
|
|
\[
{}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.758 |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.567 |
|
|
\[
{}x y^{\prime }+y = x^{3}
\] |
[_linear] |
✓ |
1.503 |
|
|
\[
{}y-x y^{\prime } = x^{2} y y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.178 |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.392 |
|
|
\[
{}\sin \left (x \right ) y+\cos \left (x \right ) y^{\prime } = 1
\] |
[_linear] |
✓ |
2.015 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
2.396 |
|
|
\[
{}x^{\prime } = x+\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.466 |
|
|
\[
{}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.733 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.210 |
|
|
\[
{}{y^{\prime }}^{2} = 9 y^{4}
\] |
[_quadrature] |
✓ |
1.503 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
18.094 |
|
|
\[
{}x^{2}+{y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.348 |
|
|
\[
{}y = x y^{\prime }+\frac {1}{y}
\] |
[_separable] |
✓ |
4.615 |
|
|
\[
{}x = {y^{\prime }}^{3}-y^{\prime }+2
\] |
[_quadrature] |
✓ |
1.017 |
|
|
\[
{}y^{\prime } = \frac {y}{x +y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.663 |
|
|
\[
{}y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\] |
[_quadrature] |
✓ |
2.437 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 4
\] |
[_quadrature] |
✓ |
0.729 |
|
|
\[
{}y^{\prime } = \frac {2 y-x -4}{2 x -y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.830 |
|
|
\[
{}y^{\prime }-\frac {y}{x +1}+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
2.040 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
15.077 |
|
|
\[
{}y^{\prime } = x y^{3}+x^{2}
\] |
[_Abel] |
✗ |
0.775 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.184 |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.884 |
|
|
\[
{}{y^{\prime }}^{3}-y^{\prime } {\mathrm e}^{2 x} = 0
\] |
[_quadrature] |
✓ |
0.654 |
|
|
\[
{}y = 5 x y^{\prime }-{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.477 |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
17.322 |
|
|
\[
{}y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.954 |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.467 |
|
|
\[
{}x^{\prime }+5 x = 10 t +2
\] |
[[_linear, ‘class A‘]] |
✓ |
2.727 |
|
|
\[
{}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.588 |
|