1. (16+x2)-xy'+32y=0 Seek a power series solution for the given differential equation about the given point x0 find the recurrence relation. So I used y=∑Anxn , found y' and y'' then I substituted it into the original equation, distributed, made all x to the n power equal to xn, made the indexes 0, and added them all up. Then I solved for an+2 and got: (an-32an-ann(n-1))/(16(n+2)(n+1))=an+2 The question asks for for the recurrence relation in the form of a2k+2 and a2k+3 which are supposed to be the recurrence relation for even and odd terms. How do I put it into that format? I'm just not sure where to go from this point. Also can someone even verify if I did the first part of obtaining an+2 correctly?