Solve the equation.

$(3x^2{y}^3+3)dx+(3x^3{y}^2-y^{-1})dy=0$

An implicit solution in the form $F(x,y)=C$ is $=C,$ where C is an arbitrary constant, and

$$ by multiplying by the integrating factor.

$($Type an expression using $x$ and $y$ as the variables.$)$