Classification of Differential Equation

Differential equation are classified according to their order.Differential equation are classified according to their order.

First Order Differential Equation

The differential equation in which only the first derivative of the unknown function appears, is called First order differential equation.

Example:

Higher Order Differential Equation

Differential equations of order 2 or more are known as Higher order differential equation.

Example:

is a higher order differential equation.

Differential equations are also classified according to their linearity and non- linearity.

Linear Differential Equation

A differential equation is said to be linear, if the unknown function and its derivatives occur only in the first degree and are not multiplied together.

Example:

Note that the degree of a linear differential equation is 1, but a differential equation whose degree is 1, need not be linear.

Example:

is a differential equation of degree 1, but it is not linear because the unknown function y and its derivative are multiplied together.

Non-linear differential equation

A differential equation which is not linear, is called non-linear.

Example:

is a non - linear differential equation because is multiplied by itself.