Answer
$\frac{dy}{dx}=\frac{-2-y}{x+3}$
Work Step by Step
Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "y" variables since we are differentiating with respect to x:
$x\frac{dy}{dx}+y+2+3\frac{dy}{dx}=0$
Move all terms with dy/dx to one side of the equation, and isolate dy/dx:
$x\frac{dy}{dx}+3\frac{dy}{dx}=-2-y$
$\frac{dy}{dx}(x+3)=-2-y$
$\frac{dy}{dx}=\frac{-2-y}{x+3}$
