Derive the Taylor series for cos t by applying the Picard method to the first-order system corresponding to the second-order initial value problem x" = -x; x(0) = 1, x'(0) =0. Please write your own answer. Don't copy another answer from Chegg.

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A: Here is the solution

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A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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A: We will find out the corresponding term.

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Q: FIND THE SOLUTION OF THE EQUATION USING THE FROBNIUS SERIES 1) ry" + 4xy' +2y 0 2) 2xy" + (x + 1)y'…

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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A: The given expression is Y=cos2x+sin2x thus the value of the series the sum of the series of cos2x…