(a) Derive the transfer function H ( s ) H ( s ) for the general first-order system given by y + y

(a) Derive the transfer function $H\left(s\right)$ for the general first-order system given by

$$\dot{y}+\sigma y=ku$$where $y\left(t\right)$ is the output, $u\left(t\right)$ is the input, and all initial conditions are assumed to be zero.

(b) Find the natural response of the first-order system.

(c) When is this system stable?

(d) Obtain the unit step response from the natural response in (b).