Link to actual problem [9004] \[ \boxed {y^{\prime }-\frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2}=0} \]
type detected by program
{"unknown"}
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 &= \frac {2}{x}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= y \,{\mathrm e}^{-\frac {x^{2}}{4}}, S \left (R \right ) &= \frac {x^{2}}{4}\right ] \\ \end{align*}