Link to actual problem [2719] \[ \boxed {2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime }=-4 \,{\mathrm e}^{2 x}} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x),G(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 {1}{\left (x -y \right )^{2}}\right ] \\ \left [R &= x, S \left (R \right ) &= -\frac {\left (x -y\right )^{3}}{3}\right ] \\ \end{align*}