Problem: Find a single uniformly valid approximation to the solution of $\epsilon y'' + x y' - y = -e^x$ with boundary conditions $y(-1)=0, y(1)=1$ in the limit $\epsilon \ll 1$. 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: $\boxed{y_{unif}(x) \approx \left[ e^x - x Ei(x) + (1 - e + Ei(1)) x \right] - \left[e^{-1} + Ei(-1) - 1 + e - Ei(1)\right] e^{-(x+1)/\epsilon}}$