|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y+x^{2} = {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.036 |
|
|
\[
{}{y^{\prime }}^{3} = y^{4} \left (y^{\prime } x +y\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
10.284 |
|
|
\[
{}\left (1-y^{\prime }\right )^{2}-{\mathrm e}^{-2 y} = {y^{\prime }}^{2} {\mathrm e}^{-2 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
14.989 |
|
|
\[
{}a x y {y^{\prime }}^{2}+\left (x^{2}-a y^{2}-b \right ) y^{\prime }-x y = 0
\] |
[_rational] |
✓ |
179.686 |
|
|
\[
{}{y^{\prime }}^{2} = \left (4 y+1\right ) \left (y^{\prime }-y\right )
\] |
[_quadrature] |
✓ |
1.061 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+b^{2}-y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.695 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}-1\right ) y^{\prime }+x y = 0
\] |
[_rational] |
✓ |
106.644 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-x y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
11.396 |
|
|
\[
{}8 {y^{\prime }}^{3} x = y \left (12 {y^{\prime }}^{2}-9\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.941 |
|
|
\[
{}4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2} = 0
\] |
[_separable] |
✓ |
0.566 |
|
|
\[
{}\left (x^{2} y^{\prime }+y^{2}\right ) \left (y^{\prime } x +y\right ) = \left (1+y^{\prime }\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✓ |
53.012 |
|
|
\[
{}y-y^{\prime } x = a \left (y^{2}+y^{\prime }\right )
\] |
[_separable] |
✓ |
1.247 |
|
|
\[
{}y-y^{\prime } x = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
0.964 |
|
|
\[
{}\left (-y+y^{\prime } x \right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\] |
[_rational] |
✓ |
135.090 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.105 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.812 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.123 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.178 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = \ln \left (x \right )^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.269 |
|
|
\[
{}y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.450 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.184 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 y^{\prime } x -8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.125 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.389 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.261 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 3 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.513 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y = x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.703 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.552 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.602 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y = x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.604 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.156 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{m}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.673 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x = \ln \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.058 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.069 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.567 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.429 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 4 x
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.664 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y = x^{2}+3 x -4
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.747 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.402 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 y^{\prime } x -8 y = x^{2}+\frac {1}{x^{2}}
\] |
[[_3rd_order, _reducible, _mu_y2]] |
✓ |
0.314 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y = x +\ln \left (x \right )
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.431 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.569 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y = x^{2} \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.303 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y = x \ln \left (x \right )
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.265 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \left (1+\ln \left (x \right )\right )^{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.735 |
|
|
\[
{}\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.883 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime } = \left (2 x +3\right ) \left (2 x +4\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.224 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.197 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} \left (y^{\prime }+y\right ) = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.297 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.473 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y = x^{2}+3 x -4
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.755 |
|
|
\[
{}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.298 |
|
|
\[
{}y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.887 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.403 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.263 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
3.065 |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = \left (x +1\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.487 |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}+y y^{\prime } = 0
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.501 |
|
|
\[
{}\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.487 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y^{\prime } \cos \left (x \right )+2 \sin \left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.412 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+3 x y = 2
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.062 |
|
|
\[
{}x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y = \ln \left (x \right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
0.697 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.390 |
|
|
\[
{}x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.812 |
|
|
\[
{}y^{\prime \prime \prime } = f \left (x \right )
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.434 |
|
|
\[
{}y^{2}+\left (2 x y-1\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\] |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.058 |
|
|
\[
{}y^{\prime \prime } = x +\sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.341 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.987 |
|
|
\[
{}y^{\prime \prime } \cos \left (x \right )^{2} = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.279 |
|
|
\[
{}x^{3} y^{\prime \prime \prime } = 1
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.210 |
|
|
\[
{}y^{\prime \prime } = \frac {a}{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.999 |
|
|
\[
{}y^{\prime \prime \prime } \csc \left (x \right )^{2} = 1
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.189 |
|
|
\[
{}y^{\prime \prime } \sqrt {a^{2}+x^{2}} = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.862 |
|
|
\[
{}x^{2} y^{\prime \prime } = \ln \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.730 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.246 |
|
|
\[
{}y^{3} y^{\prime \prime } = a
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.981 |
|
|
\[
{}y^{\prime \prime }-a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.124 |
|
|
\[
{}y^{\prime \prime }+\frac {a^{2}}{y} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.612 |
|
|
\[
{}y^{\prime \prime } = y^{3}-y
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.378 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
25.134 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.941 |
|
|
\[
{}y^{\prime \prime } = \sqrt {{y^{\prime }}^{2}+1}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.397 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.082 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.827 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.208 |
|
|
\[
{}y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.715 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +a x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.594 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x = a x
\] |
[[_2nd_order, _missing_y]] |
✓ |
34.771 |
|
|
\[
{}x y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } = 0
\] |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.408 |
|
|
\[
{}x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.263 |
|
|
\[
{}y^{\prime }-x y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.740 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.099 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.656 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.573 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.242 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.273 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.273 |
|
|
\[
{}y^{\prime \prime } = a {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.395 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.229 |
|
|
\[
{}y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}} = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
31.365 |
|
|
\[
{}a y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.219 |
|