Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' + (\ln x) y' - x(\ln x) y = 0$ with boundary conditions $y(1/2)=1, y(3/2)=1$ in the limit $\epsilon \ll 0+$ for $x>1$. 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) = e^{\frac{x^2}{2} - \frac{9}{8}} } $