Problem: Find a uniformly valid leading order approximation to the solution of $\epsilon y'' + \cosh(x)y' - e^xy = 0$ with boundary conditions $y(0) = \frac{1}{5}; y(1) = 5$ 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: $\boxed{y_{uniform}(x) = \frac{5}{e^2+1}(e^{2x} + 1) + e^{\frac{-x}{\epsilon}}(\frac{1}{5}-\frac{10}{e^2+1})}$