Problem: Find the leading order WKB approximation for the specific differential equation: $\epsilon^2 y'' = y \cosh^2 x$ with initial conditions at $y(0) = 0; y'(0) = 1$ where $\epsilon$ is a small positive parameter ($0 < \epsilon \ll 1)$. Give your final answer in a \boxed latex environment.
Solution: $\boxed{y(x) = \epsilon (\cosh x)^{-1/2} \sinh\left( \frac{1}{\epsilon} \sinh x \right)}$