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