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Solving the determine yellow in the same way of the determine r

Solving the determine yellow in the same way of the determine r

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 yellow in the same way of the determine red

e2n cn U8n-5 = a"-1(c – e)"(a – c)n ' U8n-4 = ba-1(d – f)"(b – d)n' cn+le2n U8n-3 = a"(a – c)"(c – e)n' dn+1 f2n b (b – d)"(d – f)n' e2n+1cn U8n-2 = - U8n-1 = a" (a – c)"(c – e)n f2n+1 d" br (b – d)"(d – f)r? cn+1e2n+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 = aun-1+ n = 0,1, ..., (1) Bun-14n-5 Yun-3 + đun-5 where the coefficients a, B, y, and 6 are positive real numbers and the initial con- ditions u for all i = -5, -4, ..., 0, are arbitrary non-zero real numbers. We also Un+1 = aun-1 - n= 0,1, ..., (2) present the numerical solutions via some 2D graphs. 2. ON THE EQUATION u,n+1 =Qun-1+ Bun-1un-s yun-3-bun-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+ n= 0, 1, ..., (10) Un-3 - Un-5 d" f2n-2 bn-1(b – d)n-1(d – f)n-1' e2n-1cn-1 U8n-10 = U8n-9 = 2-1(a – c)²-1(c – e)n–1' f2n-1an-1 bn-1(b – d)n-1(d – f)n-1’ U8n-8 = c"e2n-1 U8n-7 = an-1(c – e)n-1(a – c)n' d" f2n-1 bn-1 (d – f)n-1(b – d) * U8n-6 = - Furthermore, Eq. (10) gives us U8n-5U8n-9 U8n-3 = U8n-5 + U8n-7 U8n-9 e2n-1n-1 e2n c a"-1(c – e)"(a – c)" an-(c-e)"(a-c)n an-1(a-c)n-1(c-e)n-r c" e2n-1 an-1(c-e)"-'(a-c)" e2n-1cn-1 an-1(a-c)n-1(c-e)n-I e2n cn 1(c – e)*(a – c) a"(c– e)"(a – c)n-1 e2n c" an-1 а a - %3D (c - e)" (a – c)" e2n n+1 an an %3D а" (с- е)" (а — с)п"
Transcribed Image Text:e2n cn U8n-5 = a"-1(c – e)"(a – c)n ' U8n-4 = ba-1(d – f)"(b – d)n' cn+le2n U8n-3 = a"(a – c)"(c – e)n' dn+1 f2n b (b – d)"(d – f)n' e2n+1cn U8n-2 = - U8n-1 = a" (a – c)"(c – e)n f2n+1 d" br (b – d)"(d – f)r? cn+1e2n+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 = aun-1+ n = 0,1, ..., (1) Bun-14n-5 Yun-3 + đun-5 where the coefficients a, B, y, and 6 are positive real numbers and the initial con- ditions u for all i = -5, -4, ..., 0, are arbitrary non-zero real numbers. We also Un+1 = aun-1 - n= 0,1, ..., (2) present the numerical solutions via some 2D graphs. 2. ON THE EQUATION u,n+1 =Qun-1+ Bun-1un-s yun-3-bun-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+ n= 0, 1, ..., (10) Un-3 - Un-5 d" f2n-2 bn-1(b – d)n-1(d – f)n-1' e2n-1cn-1 U8n-10 = U8n-9 = 2-1(a – c)²-1(c – e)n–1' f2n-1an-1 bn-1(b – d)n-1(d – f)n-1’ U8n-8 = c"e2n-1 U8n-7 = an-1(c – e)n-1(a – c)n' d" f2n-1 bn-1 (d – f)n-1(b – d) * U8n-6 = - Furthermore, Eq. (10) gives us U8n-5U8n-9 U8n-3 = U8n-5 + U8n-7 U8n-9 e2n-1n-1 e2n c a"-1(c – e)"(a – c)" an-(c-e)"(a-c)n an-1(a-c)n-1(c-e)n-r c" e2n-1 an-1(c-e)"-'(a-c)" e2n-1cn-1 an-1(a-c)n-1(c-e)n-I e2n cn 1(c – e)*(a – c) a"(c– e)"(a – c)n-1 e2n c" an-1 а a - %3D (c - e)" (a – c)" e2n n+1 an an %3D а" (с- е)" (а — с)п"
U8n-5 U8n-9 U8n-3 = U8n-5 + U8n–7 + U8n-7-U8n-9 Dvol
Transcribed Image Text:U8n-5 U8n-9 U8n-3 = U8n-5 + U8n–7 + U8n-7-U8n-9 Dvol
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