The zero input response and zero state response are independent of each other and therefore each component can be computed independently of the other.
Zero state response varies with the system input and under zero-state conditions we could say that two independent inputs results in two independent outputs:
This document discusses zero input and zero state responses using only step inputs and only time domain analysis. If you understand, there are. The document starts with a brief review of the method of homogeneous and particular solutions (also sometimes called the natural and forced responses). The zero input and zero state solutions are then introduced. At this point using the zero input and zero state solutions will be more laborious than using the homogeneous and particular solutions, but we will develop other methods that naturally lead to zero input and zero state solutions and it is useful to see how these relate to homogeneous and particular solutions.