Solution
\(8x dx + 2xdy + 2ydx + 2ydy =0\)
\(8x + 2x \dfrac{dy}{dx} + 2y +2y \dfrac{dy}{dx}\)
\((2x+2y) \dfrac{dy}{dx} + 8x + 2y =0\)
\(\dfrac{dy}{dx} = \dfrac{-8x-2y}{2x+2y}\)
\(\dfrac{dy}{dx} = \dfrac{-4x-y}{x+y}\)