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olving the determine blue in the same way of the determine gree

olving the determine blue in the same way of the determine gree

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 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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