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Given the differential equation and its initial conditions y" + 6y' + 5y = 12 e' with y(0) = -1 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(t)} = 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" + 6y' + 5y = 12 e' with y(0) = -1 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(t)} = Y(s) L{ y'(1)} = S Y(S) - y(0) L{ y"(1)} = s2 Y(s) - Sy(0) - y'(0)

Advanced Engineering Mathematics
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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Given the differential equation and its initial conditions y" + 6y' + 5y = 12 e' with y(0) = -1 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"(t)} = S? Y(s) - Sy(0) - y'(0)
Transcribed Image Text:Given the differential equation and its initial conditions y" + 6y' + 5y = 12 e' with y(0) = -1 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"(t)} = S? Y(s) - Sy(0) - y'(0)
s2 - 25 + 5 A Y(s) = (s - 1)(s + 1)(s + 5) S BY(s) (s + 1)(s + 5) -s2 + 25 + 11 Y(s) = (s - 1)(s+ 1)(s + 5) 11 - S DY(s) (s - 1)(s + 1)(s + 5) 11 - s2 (s - 1)(s + 1) (s + 5) E Y(s) = 752 + 34S 41 Y(s) = (s - 1)(s + 1)(s + 5) F
Transcribed Image Text:s2 - 25 + 5 A Y(s) = (s - 1)(s + 1)(s + 5) S BY(s) (s + 1)(s + 5) -s2 + 25 + 11 Y(s) = (s - 1)(s+ 1)(s + 5) 11 - S DY(s) (s - 1)(s + 1)(s + 5) 11 - s2 (s - 1)(s + 1) (s + 5) E Y(s) = 752 + 34S 41 Y(s) = (s - 1)(s + 1)(s + 5) F
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