Problem: Find the leading order behavior of $\epsilon^2 y''(x) = [1 + sin(x)^2]y$ subject to boundary conditions $y(0) = 1, y'(0)=1$ in the limit of large x.
Solution: $\boxed{y(x) = \frac{1+\epsilon}{2} (1 + sin^2(x))^{-\frac{1}{4}} e^{1.2160 * x / \epsilon}}$