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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)

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)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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)
Transcribed Image Text: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)
Transcribed Image Text: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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