Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' - y'/(x^2-1.01) + ye^{-x} + sin(\epsilon)(x+cos(\epsilon)) y' = 0$ with boundary conditions $y(-1) = 1, y(1) = 1$ in the limit $\epsilon \ll 0+$. 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: $\boxed{y(x) \approx \exp(3.99 e^{-1} - (x^2 + 2x + 0.99) e^{-x}) + \left(1 - \exp(3.99 e^{-1} + 0.01 e)\right) \exp\left(-\frac{100(x+1)}{\epsilon}\right)}$