In many physical situations the relation between the rates of change of observable quantities is simpler than the relation between the quantities themselves. For this reason differential equations arise naturally as models for several problems in engineering, physical science, biological sciences and social sciences. The subject of differential equations is vast and is also of great current research interest.

Some important terms -

1. Differential Equations:

An equation containing an independent variable, a dependent variable and the derivatives of the dependent variable is called a differential Equation

Example: Each of the following equations is a differential equation

(a)    

(b)    

(c)    

(d)    

2. Order of a Differential Equation:

The order of the highest order derivative occurring in the differential Equation is called the order of the differential Equation