Answer
$\dfrac{x^{2}}{2}-2x -\ln |y+3|= c$
Work Step by Step
Given: $\dfrac{dy}{dx}=xy+3x-2y-6$
Re-arrange the given equation and integrate as follows:.
Then $ \int \dfrac{dy}{dx}=\int (x-2)(y+3) \implies \int (x-2) dx = \int \dfrac{dy}{y+3}$ ....(1)
As we know that $\int x^n dx=\dfrac{x^{n+1}}{n+1}+c$
Thus, $\dfrac{x^{1+1}}{1+1}-2x =\ln |y+3| +c$
$\dfrac{x^{2}}{2}-2x =\ln |y+3| +c$
Hence, $\dfrac{x^{2}}{2}-2x -\ln |y+3|= c$