Problem: Find the lowest-order uniform approximation to the boundary-value problem: $$ \epsilon y'' + y' \sin x + y \sin(2x) = 0 $$ with boundary conditions:$$ y(0) = \pi, \quad y(\pi) = 0 $$.
Solution: $$ \boxed{y(x) \approx \pi \, \text{erfc}\left(\frac{x}{\sqrt{2\epsilon}}\right)} $$