Problem: Find a uniformly valid leading order approximation to the solution of $\epsilon y'' + x y' + x^2 y = x^2$ 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: $\boxed{y_{unif}(x, \epsilon) = \frac{1-\text{erf}(x/\sqrt{2\epsilon})}{2} + \left(1 + e^{(1-x^2)/2}\right) \frac{1+\text{erf}(x/\sqrt{2\epsilon})}{2}}$