Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of $x$ and use implicit differentiation.

$e^{3xy}+3y=3x+2,\frac{dy}{dx}=\frac{e^{-3xy}-y}{e^{-3xy}+x}$

Use implicit differentiation to differentiate both sides of the equation $e^{3xy}+3y=3x+2.$