Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' + (1 + x^2) y' - y = 0$ with boundary conditions $y(0) = 1, y(1) = 2$ in the limit $\epsilon = 0$ from the positive direction. 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: $\boxed{y = 2 e^{\arctan(x) - \pi/4} + (1 - 2 e^{-pi/4}) e^{-x/\epsilon} }$