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A continuous time LTI system is described by (d² y(t))/dt² + 4(dy(t))/dt + 3y(t) = 2(dx(t))/dt + 4x(t) Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = e^(-2t)u(t) is given by

1. (e^(-t) - e^(-3t))u(t)
2. (e^(-t) - e^(-2t))u(t)
3. (e^(-t) + e^(-3t))u(t)
4. (e^(-t) + e^(-2t))u(t)

Correct answer: (e^(-t) - e^(-3t))u(t)

Solution

The correct option is derived from the system's response to the given input using the Laplace transform method, where the poles of the system and the input's exponential form lead to a specific combination of terms in the output. The response reflects the system's behavior characterized by its differential equation, resulting in the specified output form.

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