Find the Laplace transform of y(t)=(1−et)
Question
Find the Laplace transform of y(t)=(1−et)
Solution
The Laplace transform of a function y(t) is given by the integral from 0 to infinity of e^(-st)y(t) dt.
The Laplace transform of y(t) = (1 - e^t) is then given by:
L{y(t)} = L{1 - e^t} = L{1} - L{e^t}
The Laplace transform of 1 is 1/s, and the Laplace transform of e^t is 1/(s-1) for s > 1.
So, the Laplace transform of y(t) = (1 - e^t) is:
L{y(t)} = 1/s - 1/(s-1)
This is the Laplace transform of the function y(t) = (1 - e^t).
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