Solve the differential equation f' = 2xf2 with the initial condition f(0)=1 in the following way:
i) First, assume that there is a solution given by a power series
with a positive radius of convergence. SUbstitude this into the differential equation and figure out the coefficients an. (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)nanxn-1.
So sigma(from n=1 to infinity)nanxn-1 = 2x
I substituded x=0 into f(x) and found that a0=1
I don't really know where to go from here :S. How do I figure out the coefficients??