Introduction to Differential Equations

An equation involving one dependent variable and its derivatives with respect to one or more independent variables is called a Differential Equation.

If y = f(x) is a given function, then its derivative dy/dx can be interpreted as the rate of change of y with respect to x. In any natural process the variables involved and their rates of change are connected with one another by means of the basic scientific principles that govern the process. When this expression is written in mathematical symbols, the result is often a differential equation.

Differential equation are of two types:

  1. Ordinary
  2. Partial

Ordinary Differential Equations

An ordinary differential equation is a differential equation in which a single independent variable enters either explicitly or implicitly. For example,

dy/dx = x + 5

(y′)2 + (y′)3 + 3y = x2

d2y/dx2 − 4 dy/dx + 3y = 0