Today ABR (ABR: auditory brainstem responses) characteristics are widely and qualitatively used, and they are mainly used for clinical application of a consciousness obstacle, brain death and some consciousness level, vegetative state and so on, as the very useful inspection method. Until now, many various characteristics and models about these brain waves have been reported. But the theories and experiments of ABR are still more needed to understand the ABR characters in more details. In this paper we discussed the analysis of a differential equation model on the latency of the 5th wave of ABR, and considered the system model of generation of the type of solution of the differential equation model on the basis of an estimation of parameters of a solution of its equation model by using the Taylor series method as an iterative approximation method