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Consider the two power series Σ f(x) = x + n=0 (3x)2n+1 (2n + 1)! 8 (x + 1)" g(x) = Σ 3 n ln(n) n=2 (a) Find their radius of convergence and determine their interval of convergence. (b) Show that f(x) satisfies the equation y" = 9(y-x).

Consider the two power series Σ f(x) = x + n=0 (3x)2n+1 (2n + 1)! 8 (x + 1)" g(x) = Σ 3 n ln(n) n=2 (a) Find their radius of convergence and determine their interval of convergence. (b) Show that f(x) satisfies the equation y" = 9(y-x).

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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P2 Consider the two power series f(x) = x + (3x)2n+1 (2n + 1)! n=0 ∞ g(x) = Σ 3*nln(n)˙ (x + 1)" n=2 (a) Find their radius of convergence and determine their interval of convergence. (b) Show that f(x) satisfies the equation y" = 9(y-x).
Transcribed Image Text:P2 Consider the two power series f(x) = x + (3x)2n+1 (2n + 1)! n=0 ∞ g(x) = Σ 3*nln(n)˙ (x + 1)" n=2 (a) Find their radius of convergence and determine their interval of convergence. (b) Show that f(x) satisfies the equation y" = 9(y-x).
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