Link to actual problem [9064] \[ \boxed {y^{\prime }-\frac {\left (2 y^{\frac {3}{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{\frac {3}{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}}=0} \]
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 &= {\mathrm e}^{-x}, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{\sqrt {y}}\right ] \\ \left [R &= y^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}, S \left (R \right ) &= {\mathrm e}^{x}\right ] \\ \end{align*}