- #1
Fredh
- 10
- 0
Homework Statement
y'' - xy' + x²y = 0
Homework Equations
y = Ʃ An*x^n (from 0 to infinity)
y' = Ʃ n*An*x^n-1 (from 1 to infinity)
y'' = Ʃ n*(n-1)*An*x^n-2 (from 2 to infinity)
The Attempt at a Solution
Ʃ n*(n-1)*An*x^n-2 (from 2 to infinity) - Ʃ n*An*x^n (from 1 to infinity) + Ʃ An*x^(n+2) (from 0 to infinity) = 0
k = n-2 on the first sum, so Ʃ n*(n-1)*An*x^n-2 (2 to ∞) = Ʃ (k+2)(k+1)*Ak+2*x^k (0 to ∞)
Then, changing k back to n and joining the sums I got up to
Ʃ[(n+2)*(n+1)*An+2 - n*An]x^n + An*x^(n+2) = 0 (0 to ∞)
and I can't find out what to do with that x^(n+2), should I make n+2 = k and change the sum limits again or what?