Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' + \epsilon (x+1) y' + y^2 = 0$ with boundary conditions $y(0) = 1, y(1) = -1$ 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: $\boxed{y(x) = -\left(1 + \frac{1-x}{\sqrt{6\epsilon}}\right)^{-2}}$