|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.929 |
|
|
\[
{}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.697 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.996 |
|
|
\[
{}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.879 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.990 |
|
|
\[
{}a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
14.753 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.705 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Hermite] |
✓ |
0.460 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.558 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.775 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.489 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.468 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.153 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.666 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.104 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.772 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-y \\ y^{\prime }=2 x+y+t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.589 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y+\cos \left (2 t \right ) \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.806 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.579 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y+{\mathrm e}^{3 t} \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.555 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+5 y \\ y^{\prime }=-2 x+\cos \left (3 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.022 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{-t} \\ y^{\prime }=4 x-2 y+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.627 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.592 |
|
|
\(\left [\begin {array}{cc} 2 & 2 \\ 0 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.146 |
|
|
\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.201 |
|
|
\(\left [\begin {array}{cc} 9 & 2 \\ 2 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.143 |
|
|
\(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.106 |
|
|
\(\left [\begin {array}{cc} 2 & -3 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.180 |
|
|
\(\left [\begin {array}{cc} 6 & 0 \\ 0 & -13 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.135 |
|
|
\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.177 |
|
|
\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.102 |
|
|
\(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.141 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=-5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=11 x-2 y \\ y^{\prime }=3 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.417 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+20 y \\ y^{\prime }=40 x-19 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.423 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+2 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.391 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.687 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-6 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-11 x-2 y \\ y^{\prime }=13 x-9 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.570 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-5 y \\ y^{\prime }=10 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.390 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.384 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.412 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=13 x \\ y^{\prime }=13 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.381 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|
|
\[
{}\tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.205 |
|
|
\[
{}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.187 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.278 |
|
|
\[
{}y^{\prime } x +y = x^{3}
\] |
[_linear] |
✓ |
1.516 |
|
|
\[
{}y-y^{\prime } x = x^{2} y y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.319 |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.287 |
|
|
\[
{}y \sin \left (x \right )+y^{\prime } \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
1.830 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.992 |
|
|
\[
{}x^{\prime } = x+\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.309 |
|
|
\[
{}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.200 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
5.070 |
|
|
\[
{}{y^{\prime }}^{2} = 9 y^{4}
\] |
[_quadrature] |
✓ |
2.366 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.020 |
|
|
\[
{}x^{2}+{y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.253 |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y}
\] |
[_separable] |
✓ |
4.407 |
|
|
\[
{}x = {y^{\prime }}^{3}-y^{\prime }+2
\] |
[_quadrature] |
✓ |
0.740 |
|
|
\[
{}y^{\prime } = \frac {y}{x +y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.838 |
|
|
\[
{}y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\] |
[_quadrature] |
✓ |
1.691 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 4
\] |
[_quadrature] |
✓ |
0.549 |
|
|
\[
{}y^{\prime } = \frac {2 y-x -4}{2 x -y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.019 |
|
|
\[
{}y^{\prime }-\frac {y}{x +1}+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
1.680 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
14.960 |
|
|
\[
{}y^{\prime } = x y^{3}+x^{2}
\] |
[_Abel] |
✗ |
0.711 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.029 |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.739 |
|
|
\[
{}{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.902 |
|
|
\[
{}y = 5 y^{\prime } x -{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.421 |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
18.579 |
|
|
\[
{}y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.552 |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.361 |
|
|
\[
{}x^{\prime }+5 x = 10 t +2
\] |
[[_linear, ‘class A‘]] |
✓ |
1.609 |
|
|
\[
{}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.311 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.491 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.448 |
|
|
\[
{}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.785 |
|
|
\[
{}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right )
\] |
[_linear] |
✓ |
1.735 |
|
|
\[
{}y = x^{2}+2 y^{\prime } x +\frac {{y^{\prime }}^{2}}{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
9.293 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.835 |
|
|
\[
{}y \left ({y^{\prime }}^{2}+1\right ) = a
\] |
[_quadrature] |
✓ |
0.479 |
|
|
\[
{}x^{2}-y+\left (x^{2} y^{2}+x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.181 |
|
|
\[
{}3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.977 |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.354 |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{-x +y+1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.381 |
|
|
\[
{}y^{\prime } x -y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
2.053 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.536 |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.809 |
|
|
\[
{}\left (y^{2}-x \right ) y^{\prime }-y+x^{2} = 0
\] |
[_exact, _rational] |
✓ |
1.177 |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.848 |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.508 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.457 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.352 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
1.069 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+10 y = 100
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.439 |
|