WKB Approximation of Legendre Equation

Question

Looking at the legendre equation, I want to find the asymptotic behavior as x goes to infinity (leading order, $\nu$~O(1)) $$y''-\frac{2x}{1-x^2}y'+\frac{\nu(\nu+1)}{1-x^2}y=0$$ So I let $y=\exp(S)$ and I rearrange to get $$S''+S'^2-x^2S'^2-x^2S''-2xS'+\nu(\nu+1)=0$$ I get lost from here. Wikipedia introduces $S_0,S_i,...$. They do not really explain where these come from. I believe I want to look at the $x^2$ terms because they will be largest at x goes to infinity, but I do not see how I will get a solution.