Problem: Find a uniformly valid leading order approximation to the solution of \epsilon y'' + x y' + x y = x with boundary conditions $y(-1) = 0$, $y(1) = 1$ in the limit $\epsilon \to 0^+$. Use only the variables and constants given in the problem; do not define additional constants. The solution should be smooth, single-form expression which is valid across the entire domain. Place your final solution in a $\boxed{}$ LaTeX environment.
Solution: $\boxed{y_{unif}(x, \epsilon) = \left(1 - e^{-(x+1)}\right) \frac{1-\text{erf}(x/\sqrt{2\epsilon})}{2} + \frac{1+\text{erf}(x/\sqrt{2\epsilon})}{2}}$