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1. The problem statement, all variables and given/known data

Find the first three nonzero terms in each of two linearly indepdent solutions of the form y=[itex]\sum(c_{n}x^{n})[/itex]. Substitute known Taylor series for the analytic functions and retain enough terms to compute the necessary coefficients.

(cosx)y"+y=0

2. Relevant equations

3. The attempt at a solution

I substituted the taylor series for cosx, and the general power series into the equation, to get...

[itex]\sum(\frac{(-1)^{n}x^{2n}}{(2n)!})[/itex][itex]\sum(n(n-1)c_{n}x^{n-2})[/itex]+[itex]\sum(c_{n}x^{n})[/itex]=0

I then multiplied the first term out by series multiplication but that did not seem to get me anywhere. I am stuck at this part

By the way... for the second series (second derivative) the index begins at n=2 and the other two are n=0....sorry i do not know how to put the subscripts on the series

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# Homework Help: Differential Equation (cosx)y +y=0 using power/taylor series

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