- #1
xWaffle
- 30
- 0
Homework Statement
When solving a D.E. with power series, I've encountered something along the lines of:
[itex](2 - r)^{2}g'' = -2[/itex]
Homework Equations
Power Series
The Attempt at a Solution
I know I am just supposed to assume such a series exists, and work from there. But I'm really getting fudged up when it comes to factoring the r's back into the series, which makes the r's in the summation 2 powers higher than just 'n'.
I've reached the end where I have a recursive definition of an+1 in terms of an, but there are ridiculous fractions on the coefficients that I don't think I can generalise for values of n. They don't seem to have a pattern, and that's..a problem.
Is there an easier way to solve this, leaving the r-polynomial as it is? I expanded it and applied g'' to each term, then subbed in the second derivative of the series that represents g(x) [the standard assumed series, anrn]