Answered: Given the differential equation and its… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 25RE

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Question

q15

Given the differential equation and its initial conditions
y" - 4y' + 5y = 4 e" with y(0) = 2 and y'(0) = 7
Use the Laplace Transform rules for derivatives to convert this function into F(s) and then solve for Y(S).
L{y(1)} = Y(s)
L{ y'(1)} = S Y(S) - y(0)
L{ y"(1)} = s2 Y(s) - Sy(0) - y'(0)

2s2
7S + 7
A Y(s).
!!
(s - 3) (s + 5) (s - 1)
7s2
47S + 82
B Y(s) =
(s - 3) (s + 5)(s - 1)
2S2 - 75
Y(s) =
(s - 3) (s2 - 45 + 5)
75
26
D Y(s)
!!
(S+5)(s-1)
7s2 - 475 + 82
E Y(s)
!!
(s - 3) (s2 - 45 + 5)
2S2 - 75 + 7
Y(s) =
%3D
(s - 3) (s2 - 45 + 5)
2s2 - 75
G Y(s) =
(s - 3) (s + 5)(s - 1)

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