Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' - x y' + x^3 y = 0$ with boundary conditions $y(0) = 1$, $y(1) = 2$ in the limit $\epsilon \ll 1$. 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: $\boxed{y = e^{\frac{x^3}{3}} + (2-e^{1/3})e^{-(1-x)/\epsilon}}$