System Description

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A system is described by the following differential equation: $y''(t)+ 3y'(t)+2y = x(t)$ is initially at rest.For input x(t) = 2u(t) the output y(t) is

(a)$(1-2e^{-t} +e^-{2t})u(t)$

(b)$(1+2e^t+e^{2t})u(t-1)$

(c)$(.5 -e^t + 0.5e^{2t})u(t)$

(d)$none of above$

Answer is ( )

Concept

Type Reasoning here