In this case the 'mx' equation is a simplified manner of speaking about response of a linear device, when we want to contrast it to exponential (non-linear) response such as x^ .5, or x^2.
There may be circumstances where 'c' enters into the equation. It may be in the form of an unpredictable condition, or an external source, or non-ideal behavior of the component, etc.
However we do not necessarily need a 'c' term for every linear component, or every circumstance. Furthermore non-linear components may need a 'c' term. Then the 'c' term is not specific to linear components, and we can omit 'c'.