The polynomial \(F_n(x)= \sum _{r=0}^{n} \frac{(-1)^r \ n!}{(r!)^2(n-r)!}x^r \ \) follows which of the equation:
1
\(x \frac{d^2y}{dx^2}+(1-x)\frac{dy}{dx}+ny=0 \ \)
2
\( \frac{d^2y}{dx^2}-2x\frac{dy}{dx}+2ny=0 \ \)
3
\( x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}+(x^2-n^2)y=0 \ \)
4
\( (1-x^2)\frac{d^2y}{dx^2}-2x\frac{dy}{dx}+n(n+1)y=0 \ \)