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...
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 :(
Maybe this example may help.
Series Solutions: First Examples
What do you think?
Ohhh this makes so much more sense, so what i did was correct right?
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.