Find the Laplace transform of -5cosh(at)-7e^(mt). Find the Laplace transform of $-5\cosh(at) - 7e^{mt}$.
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We want to find the Laplace transform of $f(t)$, denoted by $F(s) = \mathcal{L}\{f(t)\}$. The Laplace transform is a linear operator, so we can write $$F(s) = \mathcal{L}\{-5\cosh(at) - 7e^{mt}\} = -5\mathcal{L}\{\cosh(at)\} - 7\mathcal{L}\{e^{mt}\}$$ Show more…
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Since 3e^(-mt) 5t cosh(at) = (-3e^(-mt))((s-m)^2)+(5(-s^2-a^2))/((s^2-a^2)^2), to find the Laplace transform of 3e^(-mt) 5t cosh(at), you negate the derivative of (-3e^(-mt))((s-m)^2)+(5(-s^2-a^2))/((s^2-a^2)^2). Therefore L{ 3e^(-mt) 5t cosh(at)} (s) = -((-3e^(-mt))((s-m)^2)+(5(-s^2-a^2))/((s^2-a^2)^2))
Adi S.
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Melissa M.
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Bcrypt_Sha256$$2B$12$We1Wwocamog01O5I.V2Tkouxdh4Ofnmgpwkor7Leaonfpu0Ubfpua B.
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