Differential Equations · Hard problem

Every solution of a certain differential equation has the form $y=x^2+Cx$ for some constant $C$. Eliminate $C$ to find $\dfrac{dy}{dx}$ in terms of $x$ and $y$, and use it to find $\dfrac{dy}{dx}$ at the point $(2,6)$ (which lies on the curve with $C=1$).