Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' - (x^2+4)y' - y^3 = 0$ with boundary conditions $y(0)=1, y(1)=\sqrt{5}$ in the limit $\epsilon \ll 0+$. Use only the variables and constants given in the problem; do not define additional constants. Solve any integrals in the final solution. Place your final solution in a $\boxed{}$ LaTeX environment.
Solution: $\boxed{y(x)=\frac{1}{\sqrt{\arctan\left(\frac{x}{2}\right)+1}}+\left(\sqrt{5}-\frac{1}{\sqrt{\arctan\left(\frac{1}{2}\right)+1}}\right)e^{-5(1-x)/\epsilon}}$