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