Link to actual problem [10138] \[ \boxed {y^{\prime } y^{\prime \prime }-y x^{2} y^{\prime }-y^{2} x=0} \]
type detected by program
{"second_order_integrable_as_is", "exact nonlinear second order ode"}
type detected by Maple
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}