Q3: Solve the following difference equations using Z-transforms: a) u[k + 2] + 4u[k + 1] + 3u[k] = (3)k , u[0] = 0, u[1] = 1 %3! Ans. :(-3)* b) y[n + 2] + 6 y[n + 1] + 9 y[n] = (2)" , y[0] = y[1] = 0 %3D Ans. ((2)"-(-3)"+

Q3: Solve the following difference equations using Z-transforms: a) u[k + 2] + 4u[k + 1] + 3u[k] = (3)k , u[0] = 0, u[1] = 1 %3! Ans. :(-3)* b) y[n + 2] + 6 y[n + 1] + 9 y[n] = (2)" , y[0] = y[1] = 0 %3D Ans. ((2)"-(-3)"+

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Q3: Solve the following difference equations using Z-transforms:
a) u[k + 2] + 4u[k + 1] + 3u[k] = (3)k , u[0] = 0,
u[1] = 1
5
(-3)k
Ans.
b) y[n + 2] + 6 y[n + 1] + 9 y[n] = (2)" , y[0] = y[1] = 0
%3!
%3D
Ans.
((2)"-(-3)" +
1(-3)")
25

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