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Input $x(t)$ and output $y(t)$ of an LTI system are related by the differential equation $y’’(t) – y’(t) – 6y(t) = x(t).$ If the system is neither causal nor stable, the impulse response $h(t)$ of the system is

  1. $\dfrac{1}{5}e^{3t}u(-t) + \dfrac{1}{5}e^{-2t}u(-t)$
  2. $-\dfrac{1}{5}e^{3t}u(-t) + \dfrac{1}{5}e^{-2t}u(-t)$
  3. $\dfrac{1}{5}e^{3t}u(-t) - \dfrac{1}{5}e^{-2t}u(t)$
  4. $-\dfrac{1}{5}e^{3t}u(-t) - \dfrac{1}{5}e^{-2t}u(t)$
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