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Theorem 19. If the solution {xn} for difference equation (1) is periodic solution , then _ (42.)" II (4")"- (49) n +k-1 In+k 2q An j=n+1 where T = 1,2, ..k + 1. As a special case , we have the following results for difference equation (2) . coro Corollary 1. The solution {xn} for difference equation (2) is periodic solution of period k if the n +k-1 following conditions satisfies: An+k II Aj = j=n+1 Corollary (5.9) If the solution {xn} for difference equation (2) is periodic solution , then n +k-1 II 4 = +k A6 j=n+1

Theorem 19. If the solution {xn} for difference equation (1) is periodic solution , then _ (42.)" II (4")"- (49) n +k-1 In+k 2q An j=n+1 where T = 1,2, ..k + 1. As a special case , we have the following results for difference equation (2) . coro Corollary 1. The solution {xn} for difference equation (2) is periodic solution of period k if the n +k-1 following conditions satisfies: An+k II Aj = j=n+1 Corollary (5.9) If the solution {xn} for difference equation (2) is periodic solution , then n +k-1 II 4 = +k A6 j=n+1

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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Show me the steps of deremine pruple and inf is here i need evey I need all the details step by step and inf is here

Theorem 19. If the solution {xn} for difference equation (1) is periodic solution , then n +k-1 II (49)": n+k II (4")"- (42.)" 2q j=n+1 where T = 1, 2, ...k + 1. As a special case , we have the following results for difference equation (2). coro Corollary 1. The solution {xn} for difference equation (2) is periodic solution of period k if the n +k-1 An+k П А, j=n+1 following conditions satisfies: Corollary(5.9) If the solution {xn} for difference equation (2) is periodic solution , then A II 4} = n +k-1 'n+k j=n+1
Transcribed Image Text:Theorem 19. If the solution {xn} for difference equation (1) is periodic solution , then n +k-1 II (49)": n+k II (4")"- (42.)" 2q j=n+1 where T = 1, 2, ...k + 1. As a special case , we have the following results for difference equation (2). coro Corollary 1. The solution {xn} for difference equation (2) is periodic solution of period k if the n +k-1 An+k П А, j=n+1 following conditions satisfies: Corollary(5.9) If the solution {xn} for difference equation (2) is periodic solution , then A II 4} = n +k-1 'n+k j=n+1
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