Chapter 7: Transcendental Functions - Section 7.4 - Exponential Change and Separable Differential Equations - Exercises 7.4 - Page 400: 20

$\dfrac{x^{2}}{2}-2x -\ln |y+3|= c$

Rewrite the given equation and then integrate. We have $ \int \dfrac{dy}{dx}=\int (x-2)(y+3)$ or, $\int (x-2) dx = \int \dfrac{dy}{y+3}$ Now, we get $(\dfrac{1}{2})x^{2}-2x =\ln |y+3| +c$ Hence, $\dfrac{x^{2}}{2}-2x -\ln |y+3|= c$