home | alphabetical index | |||||

## Differential equation
In mathematics, and more specifically calculus, a
Given that is a function of and that denote the derivatives , an The problem of solving a differential equation is to find the function whose derivatives satisfy the equation. For example, the differential equation has the general solution , where , are constants determined from boundary conditions. In the case where the equations are linear, this can be done by breaking the original equation down into smaller equations, solving those, and then adding the results back together. Unfortunately, many of the interesting differential equations are non-linear, which means that they cannot be broken down in this way. There are also a number of techniques for solving differential equations using a computer (see numerical ordinary differential equations). Ordinary differential equations are to be distinguished from partial differential equations where is a function of several variables, and the differential equation involves partial derivatives. Differential equations are used to construct mathematical models of physical phenomena such as fluid dynamics or celestial mechanics. Therefore, the study of differential equations is a wide field in both pure and applied mathematics. Differential equations have intrinsically interesting properties such as whether or not solutions exist, and should solutions exist, whether those solutions are unique. Applied mathematicians, physicists and engineers are usually more interested in how to compute solutions to differential equations. These solutions are then used to design bridges, automobiles, aircraft, sewers, etc. ## See also | |||||

copyright © 2004 FactsAbout.com |