Link to actual problem [8971] \[ \boxed {y^{\prime }-\frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_Abel, `2nd type`, `class C`], [_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 {1}{2 x}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \\ \end{align*}