The differential equation $$\exp(y)\frac{dy}{dx} = \frac{4 x + 8}{-4 \,\sin(y) + 8 \,\cos(y)}$$ 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.
$F(x,y) = G(x) + H(y) =$ .

Hint: