Problem: Find the leading order behavior of $\epsilon^2 y'' = (1+x^2)^2 y$ subject to boundary conditions $y(0) = 0$, $y'(0)= 1$ in the limit of large x.
Solution: $$\boxed{y(x) \sim \epsilon (1+x^2)^{-1/2} \sinh\left(\frac{x+x^3/3}{\epsilon}\right)}$$