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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:
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:

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 multiplied by itself. 
