In the physical world nothing is permanent except change. Differential equations are of fundamental importance because they express relationships involving rate of change. These relationships form the basis for studying the phenomena in a variety of fields in Science and engineering.
In fact, many practical laws are expressed mathematically in the form of differential equations. The primary use of differential equation is to serve as a tool for the study of change in the physical world.
A differential equation is an equation involving one dependent variable and its derivatives with respect to one or more independent variables.