Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' - y'/x - y^2 = 0$ with boundary conditions $y(0) = 1, y(1) = 1$ in the limit $\epsilon = 0$ from the positive direction. Use only the variables and constants given in the problem; do not define additional constants. Place your final solution in a $\boxed{}$ LaTeX environment. Your response should have the form of a single analytical expression.
Solution: $\boxed{y(x) = \frac{1}{\frac{1}{2}x^2 + 1} + \frac{1}{3} \exp(\frac{x-1}{\epsilon})}$