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Problem 3: Suppose that f(x) and g(x) are functions with derivatives of all orders and both of their Taylor series at æ = 0 converge at for every value of æ. If these functions satisfy s'(x) + f(æ) = e* = g'(x) + g(x), and f(0) = g'(0) = 0, find their Taylor series at r = 0. Determine if these functions are even or odd. Are these well-known functions?

Problem 3: Suppose that f(x) and g(x) are functions with derivatives of all orders and both of their Taylor series at æ = 0 converge at for every value of æ. If these functions satisfy s'(x) + f(æ) = e* = g'(x) + g(x), and f(0) = g'(0) = 0, find their Taylor series at r = 0. Determine if these functions are even or odd. Are these well-known functions?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 3: Suppose that f(x) and g(x) are functions with derivatives of all orders and both of their Taylor series at x = 0 converge at for every value of æ. If these functions satisfy f'(x) + f(x) = e* = gʻ(x) + g(x), and f(0) = g'(0) = 0, find their Taylor series at r = 0. Determine if these functions are even or odd. Are these well-known functions?
Transcribed Image Text:Problem 3: Suppose that f(x) and g(x) are functions with derivatives of all orders and both of their Taylor series at x = 0 converge at for every value of æ. If these functions satisfy f'(x) + f(x) = e* = gʻ(x) + g(x), and f(0) = g'(0) = 0, find their Taylor series at r = 0. Determine if these functions are even or odd. Are these well-known functions?
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