Link to actual problem [8931] \[ \boxed {y^{\prime }-\frac {2 a}{x^{2} \left (-y+2 F \left (\frac {y^{2} x -4 a}{x}\right ) a \right )}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
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 [R &= -\frac {-x y^{2}+4 a}{x}, S \left (R \right ) &= -\frac {y}{2 a}\right ] \\ \end{align*}