Differential equations play an important role in engineering and science. Many physical laws and relations appear in the form of differential equations. For example, the current I in an LCR circuit is described by the differential equation which is derived from Kirchhoff's laws. Similarly, the displacement y of a vibrating mass m on a spring is described by the equation my″ + ky=0. The study of differential equations involves formation of differential equations, the solutions of differential equations, and the physical interpretation of the solution in terms of the given problem.
15.1 DEFINITIONS AND EXAMPLES