Link to actual problem [13465] \[ \boxed {y^{2} {\mathrm e}^{x y^{2}}+2 x y \,{\mathrm e}^{x y^{2}} y^{\prime }=2 x} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_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 &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {{\mathrm e}^{-x \,y^{2}}}{y x}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{x y^{2}}}{2}\right ] \\ \end{align*}