|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-6 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.381 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-11 x-2 y \\ y^{\prime }=13 x-9 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-5 y \\ y^{\prime }=10 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.384 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.270 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.273 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.265 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=13 x \\ y^{\prime }=13 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.205 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.282 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.223 |
|
|
\[
{}\tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.006 |
|
|
\[
{}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.954 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.459 |
|
|
\[
{}y^{\prime } x +y = x^{3}
\] |
[_linear] |
✓ |
1.100 |
|
|
\[
{}y-y^{\prime } x = x^{2} y y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.533 |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.901 |
|
|
\[
{}\sin \left (x \right ) y+y^{\prime } \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
1.816 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.326 |
|
|
\[
{}x^{\prime } = x+\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.055 |
|
|
\[
{}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.752 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x = 0
\] |
[_separable] |
✓ |
3.576 |
|
|
\[
{}{y^{\prime }}^{2} = 9 y^{4}
\] |
[_quadrature] |
✓ |
0.753 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
8.710 |
|
|
\[
{}x^{2}+{y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.214 |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y}
\] |
[_separable] |
✓ |
3.042 |
|
|
\[
{}x = {y^{\prime }}^{3}-y^{\prime }+2
\] |
[_quadrature] |
✓ |
0.705 |
|
|
\[
{}y^{\prime } = \frac {y}{x +y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
6.250 |
|
|
\[
{}y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\] |
[_quadrature] |
✓ |
1.464 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = 4
\] |
[_quadrature] |
✓ |
0.511 |
|
|
\[
{}y^{\prime } = \frac {2 y-x -4}{2 x -y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.241 |
|
|
\[
{}y^{\prime }-\frac {y}{x +1}+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
1.554 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.141 |
|
|
\[
{}y^{\prime } = x y^{3}+x^{2}
\] |
[_Abel] |
✗ |
0.422 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
0.973 |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.083 |
|
|
\[
{}{y^{\prime }}^{3}-y^{\prime } {\mathrm e}^{2 x} = 0
\] |
[_quadrature] |
✓ |
0.471 |
|
|
\[
{}y = 5 y^{\prime } x -{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.346 |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.332 |
|
|
\[
{}y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.133 |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.724 |
|
|
\[
{}x^{\prime }+5 x = 10 t +2
\] |
[[_linear, ‘class A‘]] |
✓ |
1.238 |
|
|
\[
{}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.861 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.450 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.356 |
|
|
\[
{}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.311 |
|
|
\[
{}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right )
\] |
[_linear] |
✓ |
1.545 |
|
|
\[
{}y = x^{2}+2 y^{\prime } x +\frac {{y^{\prime }}^{2}}{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
9.994 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.672 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = a
\] |
[_quadrature] |
✓ |
0.700 |
|
|
\[
{}x^{2}-y+\left (x^{2} y^{2}+x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.086 |
|
|
\[
{}3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.071 |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.743 |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{1-x +y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.432 |
|
|
\[
{}y^{\prime } x -y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
1.930 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.616 |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.184 |
|
|
\[
{}\left (y^{2}-x \right ) y^{\prime }-y+x^{2} = 0
\] |
[_exact, _rational] |
✓ |
1.051 |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.724 |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.158 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.426 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.323 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
1.042 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+10 y = 100
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.049 |
|
|
\[
{}x^{\prime \prime }+x = \sin \left (t \right )-\cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.291 |
|
|
\[
{}y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.687 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.376 |
|
|
\[
{}y^{\prime \prime }+y = \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.091 |
|
|
\[
{}y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.187 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.069 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.676 |
|
|
\[
{}x^{3} x^{\prime \prime }+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.055 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.126 |
|
|
\[
{}{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
0.517 |
|
|
\[
{}x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.101 |
|
|
\[
{}x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x = t^{2}-3
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }+4 y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.440 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-\frac {1}{25}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.886 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.185 |
|
|
\[
{}y^{\prime \prime } = 3 \sqrt {y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.969 |
|
|
\[
{}y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.546 |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.633 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.385 |
|
|
\[
{}y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.484 |
|
|
\[
{}x^{\prime \prime }+9 x = t \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.834 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.849 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.331 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.126 |
|
|
\[
{}m x^{\prime \prime } = f \left (x\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
0.136 |
|
|
\[
{}m x^{\prime \prime } = f \left (x^{\prime }\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.274 |
|
|
\[
{}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x
\] |
[[_high_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.979 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 2 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.787 |
|
|
\[
{}x^{3} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.309 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = t^{3}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.123 |
|
|
\[
{}{y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.088 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.342 |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.244 |
|
|
\[
{}y^{\left (6\right )}-y = {\mathrm e}^{2 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.154 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.150 |
|