Since -3te^mt - 5t cosh(at) = t (-3e^mt - 5 cosh(at)), to find the Laplace transform of -3te^mt

Name: Since -3te^mt - 5t cosh(at) = t (-3e^mt - 5 cosh(at)), to find the Laplace transform of -3te^mt - 5t cosh(at) you negate the derivative of -3te^mt. Therefore L-3te^mt - 5t cosh(at)(s) = (-3)/((s-m)^2)+(5(-s^2-a^2))/((s^2-a^2)^2).
Uploaded: 2024-06-23T04:22:34-08:00
Duration: 2 min 24 s
Channel: Adi S
Description: Since -3te^mt - 5t cosh(at) = t (-3e^mt - 5 cosh(at)), to find the Laplace transform of -3te^mt - 5t cosh(at) you negate the derivative of -3te^mt. Therefore L-3te^mt - 5t cosh(at)(s) = (-3)/((s-m)^2)+(5(-s^2-a^2))/((s^2-a^2)^2).

Question

Tim Thornhill · Accepted Answer

First, we need to find the Laplace transform of each term separately.

Question

Since -3te^{mt} - 5t cosh(at) = t (-3e^{mt} - 5 cosh(at)), to find the Laplace transform of -3te^{mt} - 5t cosh(at) you negate the derivative of -3te^{mt}. Therefore L{-3te^{mt} - 5t cosh(at)}(s) = (-3)/((s-m)^2)+(5(-s^2-a^2))/((s^2-a^2)^2).

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