Problem: Find a uniformly valid approximation to the solution of $\epsilon y''(x) + (1 + x) y'(x) + 3 y(x) = 0$ with boundary conditions $y(0) = 1, y(1) = 1$ 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: $\boxed{y(x)=8(1+x)^{-3}-7e^{-\frac{x}{\epsilon}}}$