Answer
$\frac{dy}{dx}=\frac{5-2x-y}{x+2y}$
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:
$2x+x\frac{dy}{dx}+y+2y\frac{dy}{dx}-5=0$
Move all terms with dy/dx to one side of the equation, and isolate dy/dx:
$x\frac{dy}{dx}+2y\frac{dy}{dx}=5-2x-y$
$\frac{dy}{dx}(x+2y)=5-2x-y$
$\frac{dy}{dx}=\frac{5-2x-y}{x+2y}$
