Problem: Find the leading order behavior of $\epsilon y'' + cosh(x)y = -1$ subject to boundary conditions $y(-1) = 1$, $y(1) = 1$ in the limit of large x. Write your answer as a single expression for y(x) without defining any functions or variables beyond what is given in the problem. Place this answer in a single $\boxed{}$ LaTeX environment.
Solution: $\boxed{y = (1+\frac{1}{\cosh(1)}) \sec(\frac{2.1633}{2\sqrt{\epsilon}})\cos(\frac{0.00128074x^4 + 0.07861894x^3 - 0.00834220x^2 + 0.99478970x - 0.00117990}{\sqrt{\epsilon}})- \frac{1}{\cosh(x)}}$