Using z-transform methods, solve the difference equation Yk+2 - 5yk+1 + 6yk = 5 subject to yo = 0, y1 = 1 %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
9:02 O
Using z-transform methods, solve the difference
equation
Yk +2 – 5yk+1 + 6yk = 5
subject to yo = 0, y1 = 1
11. Determine Y(z).
Y(2) =
+ 6
%3D
2
z + 1
2
z + 3
Y(2)
+ 6
3
-
Z - 1
Y(2)
7
+
6
-
3
Y(2)
2
%3D
z +1
2
z + 3
12. Solve for yk-
7
+3 (3)* – 6(2)*
Yk =
7
3(3)*.
+ 6(2)*
7
(– 1)* +(- 3)* – 6( – 2)*
7
-(-1)"-국(-3)t + 6(-2)시
Yk =
3
II
Transcribed Image Text:9:02 O Using z-transform methods, solve the difference equation Yk +2 – 5yk+1 + 6yk = 5 subject to yo = 0, y1 = 1 11. Determine Y(z). Y(2) = + 6 %3D 2 z + 1 2 z + 3 Y(2) + 6 3 - Z - 1 Y(2) 7 + 6 - 3 Y(2) 2 %3D z +1 2 z + 3 12. Solve for yk- 7 +3 (3)* – 6(2)* Yk = 7 3(3)*. + 6(2)* 7 (– 1)* +(- 3)* – 6( – 2)* 7 -(-1)"-국(-3)t + 6(-2)시 Yk = 3 II
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