Problem: Find the leading order WKB approximation for the specific differential equation: $\epsilon y''(x) + (1+x)^2 y(x) = 0$ with initial conditions at $ y(0) = 0, y(1) = 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: $\boxed{y(x) \approx \frac{\sqrt{2}}{\sin\left(\frac{3}{2\sqrt{\epsilon}}\right)} \frac{1}{\sqrt{1+x}} \sin\left(\frac{x + x^2/2}{\sqrt{\epsilon}}\right)}$