Problem: Find the leading order behavior of $\frac{d^4y}{dx^4} + 2\frac{d^2y}{dx^2} + y^6 = 0, y(0)=1,y'(0)=0,y''(0)=-1,y'''(0)=-1$ in the limit $x \to \infty$. Please place your final solution in a $\boxed{}$ LaTeX Environment. If there are multiple solutions please separate them with a ;.
Solution: $\boxed{y(x) = 3.069(9.976 - x)^{-4/5} + (1 - 3.069(9.976 - x)^{-4/5})}$