Definition: Differential Equation

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 f\left(x\right) to one or more of its derivatives.

An example is:

    \[\frac{d^{2}f}{dx^{2}}+2x\frac{df}{dx}+f^{2}\left(x\right)=\sin{x}\]

This equation involves a function f 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:

    \[x\frac{d^{2}y}{dx^{2}}-\frac{dy}{dx}+xy^{2}=\sin{\left(3x\right)}\]

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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