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Use this technique to find the inverse Laplace transforms of the functions given in Exercises 7–10. 3s + 2 7. Y(s) = s2 + 25

Use this technique to find the inverse Laplace transforms of the functions given in Exercises 7–10. 3s + 2 7. Y(s) = s2 + 25

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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Please answer question 7 attached. Thank you.

In Exercises 1–6, we used the fact that L-'(aY) = « L-'(Y). However, linearity in its more general form demands that L-'@X + BY) = a L-'(X) + B L-'(Y). The form Y (s) = (2s + 5)/(s² + 4) is not available in Table 1, but if we make the adjustment S 5 2 Y (s) = 2 . s2 +4 2 s2 + 4 then, by linearity, 2 1 S y(t) = 2 L-1 + s² +4 2 S +4 = 2 cos 2t + 5 sin 2t. Use this technique to find the inverse Laplace transforms of the functions given in Exercises 7–10. 3s + 2 7. Y (s) = s² + 25
Transcribed Image Text:In Exercises 1–6, we used the fact that L-'(aY) = « L-'(Y). However, linearity in its more general form demands that L-'@X + BY) = a L-'(X) + B L-'(Y). The form Y (s) = (2s + 5)/(s² + 4) is not available in Table 1, but if we make the adjustment S 5 2 Y (s) = 2 . s2 +4 2 s2 + 4 then, by linearity, 2 1 S y(t) = 2 L-1 + s² +4 2 S +4 = 2 cos 2t + 5 sin 2t. Use this technique to find the inverse Laplace transforms of the functions given in Exercises 7–10. 3s + 2 7. Y (s) = s² + 25
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