So I'm doing some diffy eq, and I'm stuck on this simple algebraic problem.

What does (1+x^2)*x^n equal?

I was thinking x^n + x^(2n)... x^(2n+1)... which then I don't see how I could index shift that to make it only x^n. I'll write out part of the problem since it's the only part I'm confused on... if you can help just from that info stop here otherwise continue.

We'll see E[n=0] is summation of n=0 to infinity... and A>(n+2) is A sub n+2

(1+x^2)*E[n=0] (n+2)(n+1)A>(n+2)x^n

It was originally y'' = E[n=2] n(n-1)A>(n)x^(n-2) which I index shifted so it would be x^n.

Okay so now I realize that what I typed out is very confusing since I don't know LaTex, sorry guys. Basically I just want to index shift it so it's x^n, which would match the rest of the function I did not write out.