Exact Equations & Substitutions · Challenge problem

The equation $\left(\dfrac{y}{x} + 6x\right)dx + (\ln x - 2)\,dy = 0$ is exact on $x > 0$. Its solution with $y(1) = 1$, followed to the right, becomes unbounded as $x$ approaches some value $c$. Find $\displaystyle\lim_{x \to c^-} (c - x)\,y(x)$.