Problem: Find a uniformly valid approximation to the solution of $\epsilon y''(t) + (t-2) y'(t) = t$ with boundary conditions $y(0) = 1, y(1) = 0$ 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: $\boxed{y(t) = t + 2 \ln(2-t) + 1 - 2 \ln(2) - (2 - 2 \ln(2)) e^{-\frac{1-t}{\epsilon}}}$