Link to actual problem [9027] \[ \boxed {y^{\prime }-\left (1+y^{2} {\mathrm e}^{-2 x b}+y^{3} {\mathrm e}^{-3 x b}\right ) {\mathrm e}^{x b}=0} \]
type detected by program
{"abelFirstKind", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Abel]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}