How did he get the Step 2 value inside the line Taking the z-transform of (1) Z [y (k + 2) – 9y (k + 1) + 20y (k)] =Z [u (k)] = Z [y (k + 2)] - 9Z [y (k + 1)] + 20Z [y (k)] = Z =? {Y(z) – y(0) - y(1)z-} – 9z {Y(z) – y(0) {:: u sin g formula} → ? {Y(z) – 6 – 24z-1} – 9z {Y(z) – 6} + 20Y( | > Y(z) [z – 9z + 20 – 6z – 24z + 54z = %3D z) z – 9z + 20 = + 6z – 30z → Y(:)(: -4)(:- s) 6z-36z+31z z-1 Y(z) 6z2-36z+31 %3D (z-1)(z-4)(z-5)
How did he get the Step 2 value inside the line Taking the z-transform of (1) Z [y (k + 2) – 9y (k + 1) + 20y (k)] =Z [u (k)] = Z [y (k + 2)] - 9Z [y (k + 1)] + 20Z [y (k)] = Z =? {Y(z) – y(0) - y(1)z-} – 9z {Y(z) – y(0) {:: u sin g formula} → ? {Y(z) – 6 – 24z-1} – 9z {Y(z) – 6} + 20Y( | > Y(z) [z – 9z + 20 – 6z – 24z + 54z = %3D z) z – 9z + 20 = + 6z – 30z → Y(:)(: -4)(:- s) 6z-36z+31z z-1 Y(z) 6z2-36z+31 %3D (z-1)(z-4)(z-5)
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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![How did he get the
Step 2 value inside the line
Taking the z-transform of (1)
Z [y (k + 2) – 9y (k + 1) + 20y (k)] =Z [u (k)]
= Z [y (k + 2)] - 9Z [y (k + 1)] + 20Z [y (k)] = Z
=? {Y(z) – y(0) - y(1)z-} – 9z {Y(z) – y(0)
{:: u sin g formula}
→ ? {Y(z) – 6 – 24z-1} – 9z {Y(z) – 6} + 20Y(
|
> Y(z) [z – 9z + 20 – 6z – 24z + 54z =
%3D
z) z – 9z + 20 = + 6z – 30z
→ Y(:)(: -4)(:- s)
6z-36z+31z
z-1
Y(z)
6z2-36z+31
%3D
(z-1)(z-4)(z-5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ee1541-73c8-493e-8839-96c39a396882%2F12d239c2-1d61-442e-81db-a37cecd90187%2Fl1chhtp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:How did he get the
Step 2 value inside the line
Taking the z-transform of (1)
Z [y (k + 2) – 9y (k + 1) + 20y (k)] =Z [u (k)]
= Z [y (k + 2)] - 9Z [y (k + 1)] + 20Z [y (k)] = Z
=? {Y(z) – y(0) - y(1)z-} – 9z {Y(z) – y(0)
{:: u sin g formula}
→ ? {Y(z) – 6 – 24z-1} – 9z {Y(z) – 6} + 20Y(
|
> Y(z) [z – 9z + 20 – 6z – 24z + 54z =
%3D
z) z – 9z + 20 = + 6z – 30z
→ Y(:)(: -4)(:- s)
6z-36z+31z
z-1
Y(z)
6z2-36z+31
%3D
(z-1)(z-4)(z-5)
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