A differential equation is an equation that involves the derivatives of a function as well as the function itself. If partial derivatives are involved, the equation is called a partial differential equation; if only ordinary derivatives are present, the equation is called an ordinary differential equation. Differential equations play an extremely important and useful role in applied math, engineering, and physics, and much mathematical and numerical machinery has been developed for the solution of differential equations.

REFERENCES:

Arfken, G. "Differential Equations." Ch. 8 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 437-496, 1985.

Dormand, J. R. Numerical Methods for Differential Equations: A Computational Approach. Boca Raton, FL: CRC Press, 1996.