Link to actual problem [15053] \[ \boxed {y^{\prime }-2 y \,{\mathrm e}^{x}-2 \sqrt {y \,{\mathrm e}^{x}}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
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 &= \frac {{\mathrm e}^{-\frac {x}{2}+{\mathrm e}^{x}}}{2}, \underline {\hspace {1.25 ex}}\eta &= y \,{\mathrm e}^{\frac {x}{2}+{\mathrm e}^{x}}\right ] \\ \left [R &= y \,{\mathrm e}^{-2 \,{\mathrm e}^{x}}, S \left (R \right ) &= 2 \sqrt {\pi }\, \operatorname {erf}\left ({\mathrm e}^{\frac {x}{2}}\right )\right ] \\ \end{align*}