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S + 7 A Y(s) s4 (s2 + S 1) s4 + S3 + 3 B Y(s)= s3 (s2 + S - 1) s$ + s4 + 6 © r(s) s4 (s2 + S - 1) 6. O Y(s) : s4 (s? + S - 1) s2 + 3 E Y(s) s3 (s2 + $ – 1)

S + 7 A Y(s) s4 (s2 + S 1) s4 + S3 + 3 B Y(s)= s3 (s2 + S - 1) s$ + s4 + 6 © r(s) s4 (s2 + S - 1) 6. O Y(s) : s4 (s? + S - 1) s2 + 3 E Y(s) s3 (s2 + $ – 1)

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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S + 7 (A) Y(S) = s4 (s2 + S - 1) s4 + S3 + 3 B Y(s): s3 (s2 + S - 1) $5 + S4 + 6 © r(s) = s4 (s2 + S - 1) 6. DY(s). s4 (s2 + S - 1) s2 + 3 E Y(s). s3 (s2 + S - 1) S3 + S + 1 (F F Y(s) = (s2 + S - 1)
Transcribed Image Text:S + 7 (A) Y(S) = s4 (s2 + S - 1) s4 + S3 + 3 B Y(s): s3 (s2 + S - 1) $5 + S4 + 6 © r(s) = s4 (s2 + S - 1) 6. DY(s). s4 (s2 + S - 1) s2 + 3 E Y(s). s3 (s2 + S - 1) S3 + S + 1 (F F Y(s) = (s2 + S - 1)
Given the differential equation and its initial conditions y" + y' - y = t3 with y(0) = 1 and y'(0) = 0 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)} = s2 Y(s) - Sy (0) y'(0)
Transcribed Image Text:Given the differential equation and its initial conditions y" + y' - y = t3 with y(0) = 1 and y'(0) = 0 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)} = s2 Y(s) - Sy (0) y'(0)
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