Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' + (t-2) y' = t^2$ with boundary conditions $y(0) = 0, y(1) = e^{-1/3}$ 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: $\boxed{ y(x) = \frac{t^2}{2} + 2t + 4\ln \left( \frac{2-t}{2} \right) + \left( e^{-1/3} -\frac{5}{2} + 4\ln 2 \right)\exp\left( \frac{t-1}{\epsilon}\right)}$