• Consider the following difference equations: - Un+4 - 6un+3 + 14Un+2 − 16Un+1 + 8un = n (1) a) Find the general solution of the homogeneous equations associated to the dif- ference equations (1) (Hint: notice that 2 is a multiple root of the characteristic polynomial). b) Find a particular solution of the above difference equations (Hint: look for a solution of the form an + b). c) Using (a) and (b), deduce the general form of the equation (1).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Question
• Consider the following difference equations:
-
Un+4 - 6un+3 + 14Un+2 − 16Un+1 + 8un
= n
(1)
a) Find the general solution of the homogeneous equations associated to the dif-
ference equations (1) (Hint: notice that 2 is a multiple root of the characteristic
polynomial).
b) Find a particular solution of the above difference equations (Hint: look for a
solution of the form an + b).
c) Using (a) and (b), deduce the general form of the equation (1).
Transcribed Image Text:• Consider the following difference equations: - Un+4 - 6un+3 + 14Un+2 − 16Un+1 + 8un = n (1) a) Find the general solution of the homogeneous equations associated to the dif- ference equations (1) (Hint: notice that 2 is a multiple root of the characteristic polynomial). b) Find a particular solution of the above difference equations (Hint: look for a solution of the form an + b). c) Using (a) and (b), deduce the general form of the equation (1).
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