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Consider a causal $LTI$ system characterized by differential equation $\frac{dy(t)}{dt}+\frac{1}{6}y(t)=3x(t)$ The response of the system to the input $x(t)=3e^{-\frac{t}{3}}u(t)$, where $u(t)$ denotes the unit step function, is

  1. $9e^{-\frac{t}{3}}u(t)$
  2. $9e^{-\frac{t}{6}}u(t)$
  3. $9e^{-\frac{t}{3}}u(t)-6e^{-\frac{t}{6}}u(t)$
  4. $54e^{-\frac{t}{6}}u(t)-54e^{-\frac{t}{3}}u(t)$
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