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d²y dt² Use Y for the Laplace transform of y, (not Y(s)). + k²y= e^(-10t) = e -10t t, y(0) = 0, y′(0) = 0 =e^(-10t)

d²y dt² Use Y for the Laplace transform of y, (not Y(s)). + k²y= e^(-10t) = e -10t t, y(0) = 0, y′(0) = 0 =e^(-10t)

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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I need help with the first part,

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d²y dt² Use Y for the Laplace transform of y, (not Y(s)). So Y = = (s+10)(s^2+k^2) 1 (1/(100+k^2)) and y(t) = s + 10 + k² y e^(-10t) + = e -10t ‚ y(0) = 0, y′ (0) = 0 9 = e^(-10t) (-1/(100+k^2)) s+ (10/(100+k^2)) s²+k² e^(-10t)/(100+k^2)-cos(kt)/(100+k^2)+10sin(kt)/((100+k^2)k)
Transcribed Image Text:d²y dt² Use Y for the Laplace transform of y, (not Y(s)). So Y = = (s+10)(s^2+k^2) 1 (1/(100+k^2)) and y(t) = s + 10 + k² y e^(-10t) + = e -10t ‚ y(0) = 0, y′ (0) = 0 9 = e^(-10t) (-1/(100+k^2)) s+ (10/(100+k^2)) s²+k² e^(-10t)/(100+k^2)-cos(kt)/(100+k^2)+10sin(kt)/((100+k^2)k)
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