# Find a recurrence formula for the power series solution around t = 0

1. Feb 26, 2012

### s3a

1. The problem statement, all variables and given/known data
Find a recurrence formula for the power series solution around t = 0 for the differential equation:

d^2 y/dt^2 + (t - 1) dy/dt + (2t - 3)y = 0

2. Relevant equations
y = Σn=0 to inf (a_n * t^n)
and formula to differentiate polynomials.

3. The attempt at a solution
I can't find a way to bring all the sums to the same index. I've though about the fact that I can just change which index the sum is at for some of the sums because n=0 and n=1 could cause the entire term to be 0 itself but everything I think about seems to have at least one of the sums starting from another index. My attempt at a solution is attached.

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• ###### MyWork.jpg
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