Link to actual problem [11120] \[ \boxed {y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+{\mathrm e}^{\mu x} b +c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+{\mathrm e}^{\lambda x} a c +\mu \,{\mathrm e}^{\mu x} b \right ) y=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)