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e2n cn U8n-5 %3D an-1(c – e)"(a – c)n' fan an bn-1(d – f)"(b – d)n' U8n-4 cn+1e2n U8n-3 = a"(a – c)"(c – e)n dn+1 f2n b* (b – d)"(d – f)r' e2n+1cn U8n-2 U8n-1 = а" (а — с)" (с — е)»' f2n+1dn br (b – d)"(d – f)n’ cn+1e2n+1 - u8n | U8n+1

e2n cn U8n-5 %3D an-1(c – e)"(a – c)n' fan an bn-1(d – f)"(b – d)n' U8n-4 cn+1e2n U8n-3 = a"(a – c)"(c – e)n dn+1 f2n b* (b – d)"(d – f)r' e2n+1cn U8n-2 U8n-1 = а" (а — с)" (с — е)»' f2n+1dn br (b – d)"(d – f)n’ cn+1e2n+1 - u8n | U8n+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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Solve the determine blue in the same way of the determine green

U8n-6 U8n-10 U8n-4 U8n-6 + Ugn–8 + U8n-8-U8n–10
Transcribed Image Text:U8n-6 U8n-10 U8n-4 U8n-6 + Ugn–8 + U8n-8-U8n–10
e2n cn U8n-5 = n-'(c – e)"(a – c)n an- U8n-4 = bn-1 (d – f)"(b – d)"' cn+1e2n U8n-3 = a" (a – c)"(c – e)n dn+1 f2n br (b – d)"(d – f)r' e2n+1cn U8n-2 = U8n-1 = a" (a – c)"(c – e)" ' f2n+1 d" br (b – d)"(d – f)n ' cn+1e2n+1 U8n = U8n+1 = a" (c – e)*(a – c)-+I? 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 Un+1 = QUn-1+ n = 0,1, ..., (1) Yun-3 - bun-5' Bun-1un-5 run-3 + bun-5 where the coefficients a, B, y, and o 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 Un+1 = QUn-1+ Bun-1un-s Yun-3-bun-s 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 -1(6 – d)n-1(d – f)n-1' e2n-1n-1 U8n-10 = bn-1 U8n-9 = an-1(a – c)n-1(c - e)n-1' f2n-1an-1 bn-1 (b – d)n-1(d – f)n-1’ c"e2n-1 U8n-8 = U8n-7 = - an-1(c – e)n-1(a – c)n' d" fan-1 bn-1(d – f)n-1(b – d)m* U8n-6 = Moreover, it can be seen from Eq. (10) that U8n-6U8n-10 U8n-4 = U8n–6 + U8n-8 - U8n–10 d" f2n-1 bn-1(d-f)n-1(b-d)n bn-1(6-d)n-1(d-f)n-I f2n-1dn-1 d" f2n-2 d" f2n-1 br-1(d – f)"-1(b – d)" dn f2n-2 bn-1(b-d)n-1(d-f)n-T bn-1(b-d)n-T(d-f)n-T d" f2n-1 b2-1(d – f)n-1(b – d)" bn-1(d – f)n-1(b – d)" (à – }) d" f2n-2 d" f2n-1 bn-1(d – f)n-1(b - d)" ™ br-1(d – f)"(b – d)n dn+1 f2n-1 = - + br-1(d – f)"(b – d)n"
Transcribed Image Text:e2n cn U8n-5 = n-'(c – e)"(a – c)n an- U8n-4 = bn-1 (d – f)"(b – d)"' cn+1e2n U8n-3 = a" (a – c)"(c – e)n dn+1 f2n br (b – d)"(d – f)r' e2n+1cn U8n-2 = U8n-1 = a" (a – c)"(c – e)" ' f2n+1 d" br (b – d)"(d – f)n ' cn+1e2n+1 U8n = U8n+1 = a" (c – e)*(a – c)-+I? 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 Un+1 = QUn-1+ n = 0,1, ..., (1) Yun-3 - bun-5' Bun-1un-5 run-3 + bun-5 where the coefficients a, B, y, and o 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 Un+1 = QUn-1+ Bun-1un-s Yun-3-bun-s 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 -1(6 – d)n-1(d – f)n-1' e2n-1n-1 U8n-10 = bn-1 U8n-9 = an-1(a – c)n-1(c - e)n-1' f2n-1an-1 bn-1 (b – d)n-1(d – f)n-1’ c"e2n-1 U8n-8 = U8n-7 = - an-1(c – e)n-1(a – c)n' d" fan-1 bn-1(d – f)n-1(b – d)m* U8n-6 = Moreover, it can be seen from Eq. (10) that U8n-6U8n-10 U8n-4 = U8n–6 + U8n-8 - U8n–10 d" f2n-1 bn-1(d-f)n-1(b-d)n bn-1(6-d)n-1(d-f)n-I f2n-1dn-1 d" f2n-2 d" f2n-1 br-1(d – f)"-1(b – d)" dn f2n-2 bn-1(b-d)n-1(d-f)n-T bn-1(b-d)n-T(d-f)n-T d" f2n-1 b2-1(d – f)n-1(b – d)" bn-1(d – f)n-1(b – d)" (à – }) d" f2n-2 d" f2n-1 bn-1(d – f)n-1(b - d)" ™ br-1(d – f)"(b – d)n dn+1 f2n-1 = - + br-1(d – f)"(b – d)n"
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