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pply the theorem L(f* g) = L(f)L(g) to find the inverse Laplace transform; also do it in mother way when indicated (a) (-3) (also use partial fractions and the theorem L-1 (F()) = f f (7) dr) 1 b) ($²+9)²

pply the theorem L(f* g) = L(f)L(g) to find the inverse Laplace transform; also do it in mother way when indicated (a) (-3) (also use partial fractions and the theorem L-1 (F()) = f f (7) dr) 1 b) ($²+9)²

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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Question
**Apply the Theorem:** Use the theorem \(\mathcal{L}(f \star g) = \mathcal{L}(f)\mathcal{L}(g)\) to find the inverse Laplace transform. Also, perform the procedure in another way if indicated. **(a)** \(\frac{1}{s(s-3)}\) - Additionally, use partial fractions and the theorem \(\mathcal{L}^{-1}\left(\frac{F(s)}{s}\right) = \int_{0}^{t} f(\tau) d\tau\). **(b)** \(\frac{1}{(s^2+9)^2}\)
Transcribed Image Text:**Apply the Theorem:** Use the theorem \(\mathcal{L}(f \star g) = \mathcal{L}(f)\mathcal{L}(g)\) to find the inverse Laplace transform. Also, perform the procedure in another way if indicated. **(a)** \(\frac{1}{s(s-3)}\) - Additionally, use partial fractions and the theorem \(\mathcal{L}^{-1}\left(\frac{F(s)}{s}\right) = \int_{0}^{t} f(\tau) d\tau\). **(b)** \(\frac{1}{(s^2+9)^2}\)
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