In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform
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In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t).
f (t) = t sin 3t
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THEOREM 2 Differentiation of Transforms If f(t) is piecewise continuous for t≥ 0 and f(t)| ≤ Mect as t→ +∞o, then L{-tf(t)} = F' (s) for sc. Equivalently, f(1) = £¯'{F(s)} = —-—-L¯' {F'(s)}. Repeated application of Eq. (6) gives for n 1, 2, 3, .... = L{t" f(t)} = (-1)"F(n) (s) (6) (7) (8)
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Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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