Case 8. Suppose the positive integers q is even and the positive integers p,r, s are odd. In this case Sn = Sn-q and Sn+1 = Sn-p = Sn-r = Sn-s· From Equation (1), we have arb + (b+ c)¢ dp + (e+ f)¢, ф аф + (b + c)) dø + (e + f)V. Thus, døp + (e+ f)² = a¢v + (b + c)¢², (10) %3D and døp + (e + f)u? = aørp + (b+ c)b?. (11) By subtracting (10) from (11), we deduce that (e + f)(² – v²) – (b+ c)(ø² – v?) = 0. Hence, we have [(e+ f) – (b+ c)](² – v²) = 0. Since b, c, e and f are nonzero positive real numbers, and o # p. This implies [(e + f) = (b+ c)], This contradicts the condition [(e+ f) # (b+c)]. %3D
Case 8. Suppose the positive integers q is even and the positive integers p,r, s are odd. In this case Sn = Sn-q and Sn+1 = Sn-p = Sn-r = Sn-s· From Equation (1), we have arb + (b+ c)¢ dp + (e+ f)¢, ф аф + (b + c)) dø + (e + f)V. Thus, døp + (e+ f)² = a¢v + (b + c)¢², (10) %3D and døp + (e + f)u? = aørp + (b+ c)b?. (11) By subtracting (10) from (11), we deduce that (e + f)(² – v²) – (b+ c)(ø² – v?) = 0. Hence, we have [(e+ f) – (b+ c)](² – v²) = 0. Since b, c, e and f are nonzero positive real numbers, and o # p. This implies [(e + f) = (b+ c)], This contradicts the condition [(e+ f) # (b+c)]. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Show me the steps of determine red and inf is here
Transcribed Image Text:Case 8. Suppose the positive integers q is even and the positive integers p, r, s are
odd. In this case
Sn = Sn-q and Sn+1
Sn-
Sn-r
Sn-s.
From Equation (1), we have
ab + (b+ c)o
d + (e + f)o,
ao + (b+ c)
dø + (e + f)
Thus,
døp + (e + f)o? = aøry + (b+ c)o²,
(10)
and
døp + (e + f)? = aø4 + (b+ c)v².
from (11),
(11)
By subtracting
deduce that
(e + f)(6? – 2) – (b+c)(² – y?) = 0.
Hence, we have
[(e+ f) – (b+ c)I(² – 4²) = 0.
Since b, c, e and f are nonzero positive real numbers, and o + y. This implies
[(e + f) = (b+ c), This contradicts the condition [(e + f) # (b+ c).
Transcribed Image Text:The main aim of this study is to exhibit some cases on the periodic character of
the positive solutions of the rational difference equation
aSn-q + bSn-r + cSn-s
dSn
Sn+1 = Sn-p
(1)
+ eSn-r + fSn-s ) '
-q
where a, b, c, d, e, ƒ€ (0, 0). The initial conditions S-p, S-p+1;.-,S-q, S-q+1;..,S-r,
S-r+1,...,S-s,...,S_s+1,...,S_1 and So are arbitrary positive real numbers such that
p > q > r > s > 0.
е,
Expert Solution
Step 1
The mentioned steps are explained here.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
