Link to actual problem [106] \[ \boxed {{\mathrm e}^{y} x y^{\prime }-2 \,{\mathrm e}^{y}=2 \,{\mathrm e}^{2 x} x^{3}} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_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 [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{y}}{x^{2}}\right ] \\ \end{align*}