Problem: Find the leading order WKB approximation for the specific differential equation: $\epsilon^2 y'' = \frac{e^{2x}}{(1+e^x)^4} y$ 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: $\boxed{y(x) \sim 4\epsilon \cosh(x/2)\sinh\left[\frac{e^x-1}{2\epsilon(1+e^x)}\right]}$