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## Homework Statement

Solve the differential equation f' = 2xf

^{2}with the initial condition f(0)=1 in the following way:

i) First, assume that there is a solution given by a power series

f(x) =

with a positive radius of convergence. SUbstitude this into the differential equation and figure out the coefficients a

_{n}. (it is enough to guess a pattern - you do not have to prove that your guess is correct)

## The Attempt at a Solution

I know f' = sigma(from n=1 to infinity)na

_{n}x

^{n-1}.

So sigma(from n=1 to infinity)na

_{n}x

^{n-1}= 2x

I substituded x=0 into f(x) and found that a

_{0}=1

I don't really know where to go from here :S. How do I figure out the coefficients??

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