Points awarded for fastest and correct answer with work shown. Thanks! The Lapla

Question

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) =

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

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