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