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U8n-7 U8n-11 U8n-5 U8n-7 + U8n-9+ U8n-9-U8n-11

U8n-7 U8n-11 U8n-5 U8n-7 + U8n-9+ U8n-9-U8n-11

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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solving the determine red in the same way of the determine green

U8n-7 U8n-11 U8n-5 U8n-7 + U8n-9 + U8n-9-U8n–11 Evaluate
Transcribed Image Text:U8n-7 U8n-11 U8n-5 U8n-7 + U8n-9 + U8n-9-U8n–11 Evaluate
e2n cn U8n-5 = n-1(c – e)"(a – c)"' f2n dn br-1(d – f)"(b– d)n' cn+1e2n an- | U8n-4 U8n-3 = а"(а — с)" (с — е)т" dn+1 f2m b* (b – d)"(d – f)rn' e2n+1cn U8n-2 = U8n-1 = а" (а — с)" (с — е)п' f2n+1dn br (b – d)"(d – f)rn' cn+12n+1 U8n = U8n+1 a" (c – e)"(a – c)"n+1' dn+1 f2n+1 b* (d – f)"(b – d)n+1° U8n+2 = This work aims to investigate the equilibria, local stability, global attractivity and the exact solutions of the following difference equations Bun-1un-5 Yun-3 - bun-5 Un+1 = Qun–1+ n = 0,1, ..., (1) Bun-1un-5 Yun-3 + đun-5' Un+1 = aun-1 n = 0,1, ..., (2) where the coefficients a, B, , and d are positive real numbers and the initial con- ditions u; for all i = -5, –4, ..., 0, are arbitrary non-zero real numbers. We also present the numerical solutions via some 2D graphs. 2. ON THE EQUATION Un+1 = QUn-1 + Bun-1ün-5 yun-3-đun-5 This section is devoted to study the qualitative behaviors of Eq. (1). The equilibrium point of Eq. (1) is given by Un-1un-5 Un+1 = Un-1+ п 3D 0, 1, ..., (10) Un-3 - Un-5 d" f2n-2 n-1(b – d)n-1(d – f)n-1' e2n-1cn-1 U8n-10 = U8n-9 = 2²-1(a – c)n–1(c – e)z-1' f2n-1dn-1 -'(6 – d)n–1(d – f)n-1' c"e2n-1 U8n-8 = bn-1 U8n-7 an-1(c - e)n-1(a – c)n' dr f2n-1 ba-1 (d – f)"-1(b – d)" U8n-6 = U8n-7u8n-11 U8n-5 = u8n-7+ и8п-9 — и8n-11 c"e2n-1 c"e2n-2 che2n-1 n-1(c-e)n-I c"e2n-2 (а-с) an- -1(a-c)n an-i n-'(c – e)n-1(a – c)n e2n-1cn-1 (a-c)n-1(c-e)n-T e2n-2 n ar-1 (c-e)n-I c"e2n-1 -1(c - e)n-1(a – c)n an-1(c- e)n-1(a – c)* (¿ – }) e2n-1cn+1 an-. c"e2n-1 + n-'(c - e)n-1(a – c)" e2n cn an-1(c – e)"(a – c)" an. an-1(c – e)"(a – c)n*
Transcribed Image Text:e2n cn U8n-5 = n-1(c – e)"(a – c)"' f2n dn br-1(d – f)"(b– d)n' cn+1e2n an- | U8n-4 U8n-3 = а"(а — с)" (с — е)т" dn+1 f2m b* (b – d)"(d – f)rn' e2n+1cn U8n-2 = U8n-1 = а" (а — с)" (с — е)п' f2n+1dn br (b – d)"(d – f)rn' cn+12n+1 U8n = U8n+1 a" (c – e)"(a – c)"n+1' dn+1 f2n+1 b* (d – f)"(b – d)n+1° U8n+2 = This work aims to investigate the equilibria, local stability, global attractivity and the exact solutions of the following difference equations Bun-1un-5 Yun-3 - bun-5 Un+1 = Qun–1+ n = 0,1, ..., (1) Bun-1un-5 Yun-3 + đun-5' Un+1 = aun-1 n = 0,1, ..., (2) where the coefficients a, B, , and d are positive real numbers and the initial con- ditions u; for all i = -5, –4, ..., 0, are arbitrary non-zero real numbers. We also present the numerical solutions via some 2D graphs. 2. ON THE EQUATION Un+1 = QUn-1 + Bun-1ün-5 yun-3-đun-5 This section is devoted to study the qualitative behaviors of Eq. (1). The equilibrium point of Eq. (1) is given by Un-1un-5 Un+1 = Un-1+ п 3D 0, 1, ..., (10) Un-3 - Un-5 d" f2n-2 n-1(b – d)n-1(d – f)n-1' e2n-1cn-1 U8n-10 = U8n-9 = 2²-1(a – c)n–1(c – e)z-1' f2n-1dn-1 -'(6 – d)n–1(d – f)n-1' c"e2n-1 U8n-8 = bn-1 U8n-7 an-1(c - e)n-1(a – c)n' dr f2n-1 ba-1 (d – f)"-1(b – d)" U8n-6 = U8n-7u8n-11 U8n-5 = u8n-7+ и8п-9 — и8n-11 c"e2n-1 c"e2n-2 che2n-1 n-1(c-e)n-I c"e2n-2 (а-с) an- -1(a-c)n an-i n-'(c – e)n-1(a – c)n e2n-1cn-1 (a-c)n-1(c-e)n-T e2n-2 n ar-1 (c-e)n-I c"e2n-1 -1(c - e)n-1(a – c)n an-1(c- e)n-1(a – c)* (¿ – }) e2n-1cn+1 an-. c"e2n-1 + n-'(c - e)n-1(a – c)" e2n cn an-1(c – e)"(a – c)" an. an-1(c – e)"(a – c)n*
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