Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' + x y' = x \cos x$ 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: $\boxed{y = \sin x + 2 - \sin(1) \, \mathrm{erf}\left(\frac{x}{\sqrt{2\epsilon}}\right)}$