Problem: Find a uniformly valid leading order approximation to the solution of $\epsilon y'' + xy' = x \cos{x}$ with boundary conditions $y(1) = 2; y(-1) = 2$ 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: $\boxed{y(x,\epsilon) \approx 2 + \sin x - \sin 1 \erf \left(\frac{x}{\sqrt{2\epsilon}}\right)}$