|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.207 |
|
|
\(\left [\begin {array}{cc} 9 & 2 \\ 2 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.163 |
|
|
\(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.116 |
|
|
\(\left [\begin {array}{cc} 2 & -3 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.190 |
|
|
\(\left [\begin {array}{cc} 6 & 0 \\ 0 & -13 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.142 |
|
|
\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.184 |
|
|
\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.102 |
|
|
\(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.146 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.346 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=-5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.305 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=11 x-2 y \\ y^{\prime }=3 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.385 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+20 y \\ y^{\prime }=40 x-19 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.340 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+2 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.296 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.617 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-6 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.414 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-11 x-2 y \\ y^{\prime }=13 x-9 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.435 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-5 y \\ y^{\prime }=10 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.288 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.305 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.295 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=13 x \\ y^{\prime }=13 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.217 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.309 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.243 |
|
|
\[
{}\tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.261 |
|
|
\[
{}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.335 |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.128 |
|
|
\[
{}x y^{\prime }+y = x^{3}
\] |
[_linear] |
✓ |
1.300 |
|
|
\[
{}y-x y^{\prime } = x^{2} y y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.825 |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.112 |
|
|
\[
{}y \sin \left (x \right )+y^{\prime } \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
1.933 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.558 |
|
|
\[
{}x^{\prime } = x+\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.326 |
|
|
\[
{}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.721 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (y^{2}+x^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
4.377 |
|
|
\[
{}{y^{\prime }}^{2} = 9 y^{4}
\] |
[_quadrature] |
✓ |
1.745 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.203 |
|
|
\[
{}x^{2}+{y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.280 |
|
|
\[
{}y = x y^{\prime }+\frac {1}{y}
\] |
[_separable] |
✓ |
4.437 |
|
|
\[
{}x = {y^{\prime }}^{3}-y^{\prime }+2
\] |
[_quadrature] |
✓ |
0.840 |
|
|
\[
{}y^{\prime } = \frac {y}{x +y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.937 |
|
|
\[
{}y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\] |
[_quadrature] |
✓ |
2.208 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 4
\] |
[_quadrature] |
✓ |
0.632 |
|
|
\[
{}y^{\prime } = \frac {2 y-x -4}{2 x -y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.577 |
|
|
\[
{}y^{\prime }-\frac {y}{x +1}+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
1.627 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
15.441 |
|
|
\[
{}y^{\prime } = x y^{3}+x^{2}
\] |
[_Abel] |
✗ |
0.838 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.068 |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.349 |
|
|
\[
{}{y^{\prime }}^{3}-y^{\prime } {\mathrm e}^{2 x} = 0
\] |
[_quadrature] |
✓ |
0.655 |
|
|
\[
{}y = 5 x y^{\prime }-{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.471 |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
17.834 |
|
|
\[
{}y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.924 |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.823 |
|
|
\[
{}x^{\prime }+5 x = 10 t +2
\] |
[[_linear, ‘class A‘]] |
✓ |
1.459 |
|
|
\[
{}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.136 |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.530 |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.431 |
|
|
\[
{}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.365 |
|
|
\[
{}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right )
\] |
[_linear] |
✓ |
1.793 |
|
|
\[
{}y = x^{2}+2 x y^{\prime }+\frac {{y^{\prime }}^{2}}{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
10.630 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.694 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = a
\] |
[_quadrature] |
✓ |
0.507 |
|
|
\[
{}x^{2}-y+\left (y^{2} x^{2}+x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.196 |
|
|
\[
{}3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.486 |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.837 |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{y-x +1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.596 |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
1.993 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.530 |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.379 |
|
|
\[
{}\left (y^{2}-x \right ) y^{\prime }-y+x^{2} = 0
\] |
[_exact, _rational] |
✓ |
1.145 |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.523 |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.358 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.502 |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.383 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
1.126 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+10 y = 100
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.359 |
|
|
\[
{}x^{\prime \prime }+x = \sin \left (t \right )-\cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.945 |
|
|
\[
{}y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.921 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.602 |
|
|
\[
{}y^{\prime \prime }+y = \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.398 |
|
|
\[
{}y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.207 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.151 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.738 |
|
|
\[
{}x^{3} x^{\prime \prime }+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.157 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.133 |
|
|
\[
{}{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
0.570 |
|
|
\[
{}x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.115 |
|
|
\[
{}x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x = t^{2}-3
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.467 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.119 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime } = 3 \sqrt {y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.263 |
|
|
\[
{}y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.000 |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.682 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.381 |
|
|
\[
{}y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.553 |
|
|
\[
{}x^{\prime \prime }+9 x = t \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.888 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.504 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.120 |
|