Link to actual problem [4041] \[ \boxed {{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }-b y=-c} \]
type detected by program
{"clairaut"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Clairaut]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)