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