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Let a causal LTI system be characterised by the following differential equation, with initial rest condition

$\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(t)}{dt}$

where, $x(t)$ and $y(t)$ are the input and output respectively. The impulse response of the system is ($u(t)$ is the unit step function)

  1. $2e^{-2t}u(t)-7e^{-5t}u(t)$
  2. $-2e^{-2t}u(t)+7e^{-5t}u(t)$
  3. $7e^{-2t}u(t)-2e^{-5t}u(t)$
  4. $-7e^{-2t}u(t)+2e^{-5t}u(t)$
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