Initial conditions are conditions at an initial time (t=0), from which
a given set of mathematical equations or physical system evolves. The number of initial conditions that are required for a
given differential equation will depend upon the order of the differential
equation.
On the other hand, zero initial initial conditions are the initial
conditions that are zero at time t=0. For instance the distance traveled by a
runner at time t=0 is zero distance, x=0. It is where the input reference signal is zero, resulting to zero stored energy, no initial movements of parts, so the system is at rest.
