Y(2) 16z %3D Z. (2+1) (42-1) (2г—1)
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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Transcribed Image Text:How did he get the
value inside the line V
Y(z) -Y(2
2+1
2)Az-2 +
x(:) [1 - & + #) =
2z
8z2
z2+1
82-6z+1
82
2z
» Y( z
2+1
(4z-1)(2z-1)
27
» Y( z
%3D
822
z2+1
Y(z)
16z?
(z²+1)(4z-1)(2z-1)
Now partial fraction is
16z2
112
967
16
(22+1)(4z-1)(2-1)
85(+1)
85(+1)
5(27-1)
Using above in (7), we get
Y(2)
112
96z
16
32
85(+1)
85(z2+1)
5(27-1)
17(4z-1)
112z
96z2
16z
32z
> Y( z
+
5(2z-1)
%3D
85(z+1)
85(2+1)
17(4z-1
112z
96z2
8z
8z
85(z+1)
+
5(z-1/2)
85(2+1)
17(z-1/
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