If the input to an LTI system is $x(t) = e^{-3t}u(t)$ and output is $y(t) = [e^{-t} + e^{-2t}]u(t)$ Determine the system function for this system and specify the differential equation with initial rest.
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The Laplace transform of e^(-3t)u(t) can be found using the formula: L{e^(-at)u(t)} = 1/(s + a) So, the Laplace transform of x(t) is: X(s) = 1/(s + 3) Show more…
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