Problem: Find a uniformly valid approximation to the solution of $\epsilon y''(x)+(1+2x) y'(x)+8y(x)=0$ with boundary conditions $y(0)=1, y(1)=2$ 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: $\boxed{y(x) = \frac{162}{(1+2x)^4} - 161 e^{-x/ \epsilon}}$