Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' + (x^2 +1)y'+2xy=0$ with boundary conditions $y(0)=1, y(1)=5$ in the limit $\epsilon = 0$ from the positive direction. 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: $\boxed{y(x) = \frac{10}{x^2+1} + e^{\frac{-x}{\epsilon}} - 10e^{\frac{-x}{\epsilon}}}$