Consider a system model given by

$\frac{d^{2}x(t)}{d{t}^2}+4\frac{dx(t)}{dt}+5x(t)=2\frac{df(t)}{dt}+f(t)$

$x(0)=1$

$\frac{dx(t)}{dt}{|}_t|=0=1$

What is the impulse response function?

$3e^{-2t}sint+e^{-2t}cost+2$

$e^{-2t}sint+e^{-2}cost$

$-4e^{-2t}sint-2e^{-2}cost+2$

$e^{-2t}(2cost-3sint)$

$sint-2cost+e^{-t}$

$3e^{-2}sint+e^{-2t}cost$