Problem: Find a uniformly valid leading order approximation to the solution of $\epsilon y'' + x y' = 0$ with boundary conditions $y(-1) = 1$, $y(1) = 2$ 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: $\boxed{y = \frac{1}{2} \text{erf}\left(\frac{x}{\sqrt{2\epsilon}}\right) + \frac{3}{2}}$