Link to actual problem [925] \[ \boxed {{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right )=\frac {1}{x^{2}}} \]
type detected by program
{"exact"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
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}^{-y^{2}}}{x^{2} y}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{y^{2}} x^{2}}{2}\right ] \\ \end{align*}