Problem: Find the leading order behavior of $\epsilon^2 y'' = (1/x^2) y$ subject to boundary conditions $y(1) = 1$, $y'(1)= 0$ in the limit of large x.
Solution: $\boxed{y(x) \sim x^{1/2}[(\frac{1}{2}-\frac{\epsilon}{4})x^{1/\epsilon}+(\frac{1}{2}+\frac{\epsilon}{4})x^{-1/\epsilon}]}$