Chapter 2 - Differentiation - 2.5 Exercises - Page 145: 5

$\dfrac{dy}{dx}=\dfrac{3x^2-y}{x-2y}.$

$\dfrac{d}{dx}(x^3)-\dfrac{d}{dx}(xy)+\dfrac{d}{dx}(y^2)=\dfrac{d}{dx}(7)\rightarrow$ $3x^2-(y+x\dfrac{dy}{dx})+\dfrac{dy}{dx}(2y)=0\rightarrow$ $\dfrac{dy}{dx}(x-2y)=3x^2-y\rightarrow$ $\dfrac{dy}{dx}=\dfrac{3x^2-y}{x-2y}.$