Find the recursion formula for the following equation at x=0, and find the first four nonzero terms with the solution y(0)=-6 and y'(0)=2.
(3-x)y'' + x^2 y' + (1+x)y = 0

Question

￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼Find the recursion formula for the following equation at x=0, and find the first four nonzero terms with the solution y(0)=-6 and y'(0)=2. 
(3-x)y'' + x^2 y' + (1+x)y = 0

anonymous · Answer

I understand how to do recursion formulas and finding terms, i am just not sure what I need to do with y(0) = -6 and y'(0) = 2.

mathmale · Answer

Once you have found the required recursion formula, the given "y(0) = -6 and y'(0) = 2" are the necessary initial values.

I'd suggest you explain precisely what you mean by "recursion formulas"  Are you by any chance applying Newton's Method for finding roots?  If not, what?

anonymous · Answer

I don't believe I should be ..
I think I'm am simply supposed to use the definition of a power series, replace that for while and solve for a recursive formula, y and then differentiate. Then I'll use the initial values.
Does this sound like a reasonable method or do you have another method which may be easier?