First
Order System Descriptions
A first order system has a differential equation  given below.

tdx/dt
+ x(t) = G_{dc}u(t)
With this differential equation, the terms are:

x(t) =
Response of the System,

u(t) =
Input to the System,

t
= The System Time Constant,

G_{dc}
= The DC Gain of the System.
If the differential equation is Laplace transformed we get:

tX(s)
+ X(s) = G_{dc}U(s), or, solving for the transfer function,
we get:

Transfer Function = X(s)/U(s)
= G_{dc}/(st
+ 1)