Link to actual problem [4048] \[ \boxed {{y^{\prime }}^{2}-y^{\prime } y=-{\mathrm e}^{x}} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 1, \underline {\hspace {1.25 ex}}\eta &= \frac {y}{2}\right ] \\ \left [R &= y \,{\mathrm e}^{-\frac {x}{2}}, S \left (R \right ) &= x\right ] \\ \end{align*}