Some Examples of Application of Differential Equation

Abstract

A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play an important role in many disciplines including engineering, physics, economics, and biology. Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the manners of complex systems. In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. The aim of study is not limited to mathematics and physics only, but variety of problems, decomposition of radioactive substances like in chemistry, the growth rate of bacteria and virus in biology, the rate of spreading infectious diseases in medical science. The most difficult problem of social science the rate of increase of population or the relation between demand and supply in commerce and calculation of interest on principle amount can be expressed in the form of a differential equation