# Recurrance relaltion

• Aug 26th 2010, 10:45 PM
vipertongn
Recurrance relaltion
The problem statement, all variables and given/known data

Find the recurrence relation for the following diﬀerential equation. You
do not need to solve the rest of the way.

y" − 2xy = 0

The attempt at a solution

I'm not exactly sure how to do this problem but from the example of the book I tried this:

kinda ended up with
(k+1)(k+2)ck+2+2ck-1= 0 k=1,2,3...
• Aug 26th 2010, 11:25 PM
pickslides
• Aug 26th 2010, 11:32 PM
vipertongn
ok by adding two power series i get

sigma: CnX^n-2*n(n-1)+2X Sigma: CnX^n
then make k=x-2 for one and simultaneously have k=x+1 and substitute
and then I kinda get lost from there. I just based it off of a book, I'm not sure how to run this problem :(
• Aug 26th 2010, 11:55 PM
pickslides
Maybe this example may help.

Series Solutions: First Examples

What do you think?
• Aug 27th 2010, 12:00 AM
vipertongn
Ohhh this makes so much more sense, so what i did was correct right?
• Aug 27th 2010, 12:17 AM
pickslides
Just be careful with your general solution as you have a function of x in the coefficent of y the example does not have that.