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Hence, Ck obeys the difference equation (1 ). 1 7 3 +... (7.99) Ck+1 = + Ck. 2k 24k2 16k3 APPLICATIONS 227 The dominant behavior of ck can be found by considering (1 1 Ck+1 ~ (7.100) 2k Trying a solution of the form Ck ~ Ak", (7.101) where A is an arbitrary constant and a is to be determined, gives 1 kª. 2k (k + 1)" (7.102) Now (k + 1)“ = k° (1+)"~ K° (1 + ). (7.103)

Hence, Ck obeys the difference equation (1 ). 1 7 3 +... (7.99) Ck+1 = + Ck. 2k 24k2 16k3 APPLICATIONS 227 The dominant behavior of ck can be found by considering (1 1 Ck+1 ~ (7.100) 2k Trying a solution of the form Ck ~ Ak", (7.101) where A is an arbitrary constant and a is to be determined, gives 1 kª. 2k (k + 1)" (7.102) Now (k + 1)“ = k° (1+)"~ K° (1 + ). (7.103)

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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Hence, c obeys the difference equation 1 7 3 + 16k3 Ck+1 = (7.99) .. 2k 24k2 APPLICATIONS 227 The dominant behavior of Ck can be found by considering 1 2k 1 Ck. (7.100) Ck+1 ~ Trying a solution of the form Ak", (7.101) where A is an arbitrary constant and a is to be determined, gives (1-). (k + 1)ª . k°. 2k (7.102) Now (R + 1)* = k° (1+ )" ~ k* (1+;). ~ ka ( 1 (7.103)
Transcribed Image Text:Hence, c obeys the difference equation 1 7 3 + 16k3 Ck+1 = (7.99) .. 2k 24k2 APPLICATIONS 227 The dominant behavior of Ck can be found by considering 1 2k 1 Ck. (7.100) Ck+1 ~ Trying a solution of the form Ak", (7.101) where A is an arbitrary constant and a is to be determined, gives (1-). (k + 1)ª . k°. 2k (7.102) Now (R + 1)* = k° (1+ )" ~ k* (1+;). ~ ka ( 1 (7.103)
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