Link to actual problem [8921] \[ \boxed {y^{\prime }-\frac {\left (x^{\frac {3}{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2}=0} \]
type detected by program
{"unknown"}
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 [\underline {\hspace {1.25 ex}}\xi &= \frac {1}{\sqrt {x}}, \underline {\hspace {1.25 ex}}\eta &= \frac {x^{\frac {3}{2}}}{2}\right ] \\ \left [R &= y-\frac {x^{3}}{6}, S \left (R \right ) &= \frac {2 x^{\frac {3}{2}}}{3}\right ] \\ \end{align*}