Link to actual problem [10164] Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime }+x \left (y-1\right ) y^{\prime \prime }+x \left (y^{\prime }\right )^{2}+\left (1-y\right ) y^{\prime }=0} \end {gather*}
type detected by program
{"unknown"}
type detected by Maple
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}