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)
- $2e^{-2t}u(t)-7e^{-5t}u(t)$
- $-2e^{-2t}u(t)+7e^{-5t}u(t)$
- $7e^{-2t}u(t)-2e^{-5t}u(t)$
- $-7e^{-2t}u(t)+2e^{-5t}u(t)$