Problem: Find a uniformly valid approximation to the solution of $\epsilon y''(x) + (2 - x^2) y'(x) + 4 y(x) = 0$ with boundary conditions $y(0) = 0, y(1) = 2$, in the limit $\epsilon \to 0$. 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: $\boxed{y(x)=2(3+2\sqrt{2})^\sqrt{2}((\frac{\sqrt{2}-x}{\sqrt{2}+x})^\sqrt{2}-e^{-\frac{2x}{\epsilon}})}$