Problem: Find the leading order WKB approximation for the specific differential equation: $\epsilon^2 y''(x) = \cot((x-\pi/2+0.25)/100)y(x)$ with initial conditions at $y(0) = 1,y'(0) = 1$ 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) = (\frac{\pi/2 - 0.25 - x}{\pi/2 - 0.25})^{1/4} \cos(\frac{20}{\epsilon}(\sqrt{\pi/2 - 0.25} - \sqrt{\pi/2 - 0.25 - x})) + \epsilon\frac{(\pi/2 - 0.25)^{1/4}(\pi/2 - 0.25 - x)^{1/4}}{10} \sin(\frac{20}{\epsilon}(\sqrt{\pi/2 - 0.25} - \sqrt{\pi/2 - 0.25 - x}))} $