Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
U8n-2 U8n-6 U8n U8n-2 + U8n-4 + U8n-4-U8n-6

U8n-2 U8n-6 U8n U8n-2 + U8n-4 + U8n-4-U8n-6

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
See similar textbooks
icon
Related questions
Question
e2n cn an-1(c- e)"(a – c)n' U8n-5 = | U8n-4 = b2-1(d – f)"(b – d)n' cn+1e2n U8n-3 = а" (а — с)"(с — е)п' dn+1 f2n b* (b – d)"(d – f)"' e2n+1cn U8n-2 = U8n-1 = a" (а — с)"(с — е)т" U8n br (b – d) (d – f) cn+1e2n+1 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-1un-5 Un+1 = aun-1 - n = 0,1, ..., (2) Yun-3 + dun-5 where the coefficients a, B, y, and & 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 = aun-1 + Bun-1ün-s yun-3-óun-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 br-1(b – d)n-1(d – f)n-1' U8n-10 = e2n-1cn-1 U8n-9 = an-1(a – c)n-1(c - e)r-I' f2n-1dn-1 bn-1(b – d)n-1(d – f)n-1' c"e2n-1 an-1(c – e)n-1(a – c)n' d" f2n-1 b2-1(d-f)n-1(b– d)n U8n-8 = U8n-7 = U8n-6 U8n-2u8n-6 U8n = U8n-2 + U8n-4 - U8n-6 d" f2n-1 u(f-P)u(P-9)u4 bn-1(d-f)n-1(b-d)" (- dn+1 f2n dn+1 f2n d" f2n–1 bn-1(d-f)n-'(6-d)" fan dn /)" (b-d)n d" f2n br (b – d)" (d – f)"-I b" (b – d)" (d – f)" dn+1 f2n b" (b – d)" (d – f)" d" f2n+1 b" (b – d)" (d – f)"* Other solutions can be similarly proved.
Transcribed Image Text:e2n cn an-1(c- e)"(a – c)n' U8n-5 = | U8n-4 = b2-1(d – f)"(b – d)n' cn+1e2n U8n-3 = а" (а — с)"(с — е)п' dn+1 f2n b* (b – d)"(d – f)"' e2n+1cn U8n-2 = U8n-1 = a" (а — с)"(с — е)т" U8n br (b – d) (d – f) cn+1e2n+1 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-1un-5 Un+1 = aun-1 - n = 0,1, ..., (2) Yun-3 + dun-5 where the coefficients a, B, y, and & 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 = aun-1 + Bun-1ün-s yun-3-óun-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 br-1(b – d)n-1(d – f)n-1' U8n-10 = e2n-1cn-1 U8n-9 = an-1(a – c)n-1(c - e)r-I' f2n-1dn-1 bn-1(b – d)n-1(d – f)n-1' c"e2n-1 an-1(c – e)n-1(a – c)n' d" f2n-1 b2-1(d-f)n-1(b– d)n U8n-8 = U8n-7 = U8n-6 U8n-2u8n-6 U8n = U8n-2 + U8n-4 - U8n-6 d" f2n-1 u(f-P)u(P-9)u4 bn-1(d-f)n-1(b-d)" (- dn+1 f2n dn+1 f2n d" f2n–1 bn-1(d-f)n-'(6-d)" fan dn /)" (b-d)n d" f2n br (b – d)" (d – f)"-I b" (b – d)" (d – f)" dn+1 f2n b" (b – d)" (d – f)" d" f2n+1 b" (b – d)" (d – f)"* Other solutions can be similarly proved.
O Tap to view steps... U8n-2 U8n-6 U8n = U8n-2 + U8n-4 + U8n-4 U8n-6
Transcribed Image Text:O Tap to view steps... U8n-2 U8n-6 U8n = U8n-2 + U8n-4 + U8n-4 U8n-6
Expert Solution
steps

Step by step

Solved in 6 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS