Definition 1: Krantz, S.G. (2005). Differential Equations Demystified: A Self-Teaching Guide. New York: McGraw-Hill. (p. 1-2)
A differential equation is an equation relating some function to one or more of its derivatives.
An example is:
This equation involves a function together with its first and second derivatives.
Definition 2: O’Neil, P.V. (1995). Advanced Engineering Mathematics (4th ed.). Boston: PWS Publishing Company. (p. 2)
A differential equation is an equation that contains one or more derivatives. For example: