Problem: Find a uniformly valid approximation to the solution of $\epsilon y''+\frac{y'}{x}+y=0$ with boundary conditions $[y(-1)=2e^{-1/2}, y(1)=e^{-1/2}]$ in the limit $\epsilon \rightarrow 0+$. 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: $\boxed{y(x)=\left(\frac{3-x}{2}\right)e^{-\frac{x^2}{2}}}$