Problem: Find a uniformly valid approximation, with error of order $\epsilon^2$, to the solution of $\epsilon y'' + y' +y = 0$ with boundary conditions $y(0) = e, y(1) = 1$ in the limit $\epsilon = 0$ from the positive direction. Notice that there is no boundary layer in leading order, but one does appear in next order. 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: $\boxed{y = e^{1-x} + \epsilon[(-x+1)e^{1-x} -e^{1-\frac{x}{\epsilon}}]}$