Points awarded for fastest and correct answer with work shown. Thanks! The Lapla
ID: 2969629 • Letter: P
Question
Points awarded for fastest and correct answer with work shown. Thanks! The Laplace transform of the systemy'' - 4y' + 3y = e2t, y(0) = 2; y'(0) = -1
would produce a transform Y(s) =
Question 8 options: A) (s2 - 5s + 7)/[(s - 2)(s2 - 4s + 3)] B) (s2 - 7s + 13)/[(s - 2)(s2 - 4s + 3)] C) (2s2 - 11s + 15)/[(s - 2)(s2 - 4s + 3)] D) (2s2 - 13s + 19)/[(s - 2)(s2 - 4s + 3)] E) (2s2 - 10s + 13)/[(s - 2)(s2 - 4s + 3)] F) (s2 - 4s + 5)/[(s - 2)(s2 - 4s + 3)] G) (s2 - 3s + 3)/[(s - 2)(s2 - 4s + 3)] H) (s2 - 8s + 13)/[(s - 2)(s2 - 4s + 3)] I) (3s2 - 17s + 23)/[(s - 2)(s2 - 4s + 3)] J) (3s2 - 19s + 27)/[(s - 2)(s2 - 4s + 3)] K) (3s2 - 16s + 21)/[(s - 2)(s2 - 4s + 3)] L) (3s2 - 20s + 29)/[(s - 2)(s2 - 4s + 3)] M) none of these Points awarded for fastest and correct answer with work shown. Thanks! Points awarded for fastest and correct answer with work shown. Thanks! The Laplace transform of the system
y'' - 4y' + 3y = e2t, y(0) = 2; y'(0) = -1
would produce a transform Y(s) =
The Laplace transform of the system
y'' - 4y' + 3y = e2t, y(0) = 2; y'(0) = -1
would produce a transform Y(s) =
A) (s2 - 5s + 7)/[(s - 2)(s2 - 4s + 3)] B) (s2 - 7s + 13)/[(s - 2)(s2 - 4s + 3)] C) (2s2 - 11s + 15)/[(s - 2)(s2 - 4s + 3)] D) (2s2 - 13s + 19)/[(s - 2)(s2 - 4s + 3)] E) (2s2 - 10s + 13)/[(s - 2)(s2 - 4s + 3)] F) (s2 - 4s + 5)/[(s - 2)(s2 - 4s + 3)] G) (s2 - 3s + 3)/[(s - 2)(s2 - 4s + 3)] H) (s2 - 8s + 13)/[(s - 2)(s2 - 4s + 3)] I) (3s2 - 17s + 23)/[(s - 2)(s2 - 4s + 3)] J) (3s2 - 19s + 27)/[(s - 2)(s2 - 4s + 3)] K) (3s2 - 16s + 21)/[(s - 2)(s2 - 4s + 3)] L) (3s2 - 20s + 29)/[(s - 2)(s2 - 4s + 3)] M) none of these A) (s2 - 5s + 7)/[(s - 2)(s2 - 4s + 3)] B) (s2 - 7s + 13)/[(s - 2)(s2 - 4s + 3)] C) (2s2 - 11s + 15)/[(s - 2)(s2 - 4s + 3)] D) (2s2 - 13s + 19)/[(s - 2)(s2 - 4s + 3)] E) (2s2 - 10s + 13)/[(s - 2)(s2 - 4s + 3)] F) (s2 - 4s + 5)/[(s - 2)(s2 - 4s + 3)] G) (s2 - 3s + 3)/[(s - 2)(s2 - 4s + 3)] H) (s2 - 8s + 13)/[(s - 2)(s2 - 4s + 3)] I) (3s2 - 17s + 23)/[(s - 2)(s2 - 4s + 3)] J) (3s2 - 19s + 27)/[(s - 2)(s2 - 4s + 3)] K) (3s2 - 16s + 21)/[(s - 2)(s2 - 4s + 3)] L) (3s2 - 20s + 29)/[(s - 2)(s2 - 4s + 3)] M) none of these A) (s2 - 5s + 7)/[(s - 2)(s2 - 4s + 3)] B) (s2 - 7s + 13)/[(s - 2)(s2 - 4s + 3)] C) (2s2 - 11s + 15)/[(s - 2)(s2 - 4s + 3)] D) (2s2 - 13s + 19)/[(s - 2)(s2 - 4s + 3)] E) (2s2 - 10s + 13)/[(s - 2)(s2 - 4s + 3)] F) (s2 - 4s + 5)/[(s - 2)(s2 - 4s + 3)] G) (s2 - 3s + 3)/[(s - 2)(s2 - 4s + 3)] H) (s2 - 8s + 13)/[(s - 2)(s2 - 4s + 3)] I) (3s2 - 17s + 23)/[(s - 2)(s2 - 4s + 3)] J) (3s2 - 19s + 27)/[(s - 2)(s2 - 4s + 3)] K) (3s2 - 16s + 21)/[(s - 2)(s2 - 4s + 3)] L) (3s2 - 20s + 29)/[(s - 2)(s2 - 4s + 3)] M) none of these
Explanation / Answer
formula:
L{y'} = sY(s) - y(0)
L{y''} = s^2Y(s) - sy(0) - y'(0)
y'' - 4y' + 3y = e^(2t)
apply laplace we get
s^2Y(s) - sy(0) - y'(0) - 4sY(s) + 4y(0) + 3Y(s) = 1/(s-2)
put y(0) = 2; y'(0) = -1
s^2Y(s) - 2s +1 - 4sY(s) + 8 + 3Y(s) = 1/(s-2)
=>
Y(s)*[s^2 - 4s + 3] = 1/(s-2) + 2s - 9
=>
Y(s) = [2s^2 - 13s + 18]/[(s-2)(s^2 - 4s + 3)]
M) none of these