?

Differential Equations

Free Version

Upgrade subject to access all content

Moderate

An ODE with Nonconstant Coefficients: Recurrence Relation

DIFFEQ-RXIJVE

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

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

B

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

C

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

D

None of the above