Problem: Find a uniformly valid approximation to the solution of $ \epsilon y''(x) + (x-1)^2 y'(x) - x(x-1)^2 y(x) = \epsilon x^2 \sin(\pi x) [1+y(x)] $ with boundary conditions $y(1/2)=3, y(3/2)=3$ 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: $$\boxed{y(x) \approx 3 e^{x^2/2 - 9/8} + 3(1 - e^{-1}) e^{-(x-1/2)/(4*\epsilon)}}$$