Link to actual problem [10091] \[ \boxed {2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y^{\prime } y=0} \]
type detected by program
{"second_order_nonlinear_solved_by_mainardi_lioville_method"}
type detected by Maple
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x \,\textit {\_y1}^{2}}\right ] \\ \end{align*}