Link to actual problem [4673] \[ \boxed {x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime }=0} \]
type detected by program
{"second_order_integrable_as_is", "second_order_nonlinear_solved_by_mainardi_lioville_method"}
type detected by Maple
[[_2nd_order, _exact, _nonlinear], _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 {\ln \left (y\right )}{\textit {\_y1}^{2}}\right ] \\ \end{align*}