Definitions Differential Equations

 

Definition 1 (Differential Equation)

A differential equation is a relation between the independent, dependent variables and their differential coefficients.

Example:

Definition 2 (Order of Differential Equation)

The order of differential equation is defined to be the order of the highest order derivative of the dependent variable occurring in the differential equation.

Example:

Definition 3 (Degree of a Differential Equation)

The degree of a differential equation is the highest power of the highest order derivative after making the equation free from radicals and fractional indices as far as the derivatives are concerned.

In other words, the degree of a differential equation whose terms are polynomial in the derivatives is the highest power (positive integral index) of the highest order derivative in it.

Examples:

(i) Order = 2 degree = 3

(ii) Order =1 degree = 2

(iii) Order =1 degree = 2