Problem: Find the leading order WKB approximation for the specific differential equation: $\epsilon^2 y'' - (1+x)^2 y = 0$ with initial conditions at $y(0) = 1, y(1) = e^{-1}$ where $\epsilon$ is a small positive parameter ($0 < \epsilon \ll 1$). Use only the variables and constants given in the problem; do not define additional constants. Place your final solution in a $\boxed{}$ LaTeX environment.
Solution: $\boxed{y(x)\sim \frac{(1+x)^{-1/2}}{e^{3/(2\epsilon)}-e^{-3/(2\epsilon)}} [(\sqrt{2}e^{-1}-e^{-3/(2\epsilon)})\exp((x + x^2/2)/\epsilon) +(e^{3/(2\epsilon)}-\sqrt{2}e^{-1})\exp(-(x + x^2/2)/\epsilon)]}$