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Jack is solving $(2-x^2)y''+y=0$ by seeking solutions of the form $y(x)=\sum_{n=0}^{\infty}a_nx^n$.

The recurrence relation Jack may find is:

$a_{n+2}=-\cfrac{a_n}{(2-x^2)(n+2)(n+1)}$

$a_{n+2}=-\cfrac{a_n}{(n+2)(n+1)}$

$a_{n+2}=\frac{n^2-n-1}{2(n+2)(n+1)}a_n$

None of the above