Differential equation

In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. Differential equations form the basic language of physics.

Differential equations are divided into two types:

• An ordinary differential equation (ODE) only contains functions of one variable, and derivatives in that variable.
• A partial differential equation (PDE) contains multivariate functions and their partial derivatives.

The order of a differential equation is that of the highest derivative that it contains. For instance, a first-order differential equation contains only first 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.

External links

• Polyanin, Andrei: EqWorld: The World of Mathematical Equations. An online resource focusing on ordinary differential, partial differential (mathematical physics), integral, and other mathematical equations.