Link to actual problem [10426] \[ \boxed {y^{\prime }-{\mathrm e}^{\mu x} \left (y-b \,{\mathrm e}^{\lambda x}\right )^{2}=b \lambda \,{\mathrm e}^{\lambda x}} \]
type detected by program
{"riccati"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \left [R &= y-b \,{\mathrm e}^{\lambda x}, S \left (R \right ) &= \frac {{\mathrm e}^{\mu x}}{\mu }\right ] \\ \end{align*}