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