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• 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).

• 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).

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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• 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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