Problem: Find a uniformly valid leading order approximation to the solution of $\epsilon y + \sqrt(x) y' - y = 0$ with boundary conditions $y(0)=0, y(1)=e^2$ 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: $\boxed{ e^{2\sqrt{x}} - 1 + \frac{\int_0^{\frac{x}{\epsilon^{2/3}}} e^{-\frac{2}{3}s^{3/2}} \, ds}{\left(\frac{2}{3}\right)^{1/3} \Gamma\left(\frac{2}{3}\right)} }$