a$.$ A system has an output $y(t)$ which varies with time when subject to step input of $u(t)$ and is described by the following equation. Find the time response of the system if a unity step input $u(t)=1$ is applied to it and the initial conditions are $y(0)=1$ and $\frac{dy(0)}{dt}=0.$

$\frac{d^{2}y}{d{t}^2}+5\frac{dy}{dt}+4y(t)=5u(t)$