The differential equation $$18 \,\frac{dy}{dx} = (9 - x^2)^{-1/2}\,\exp(- 6 y)$$ has an implicit general solution of the form $F(x,y) = K.$
In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form $$F(x,y) = G(x) + H(y) =K.$$
Find such a solution and then give the related functions requested.
$F(x,y) = G(x) + H(y) =$ .