Ordinary D.F equations, their order and degree

Differential equation: An equation containing an independent variable, dependent variable and differential coefficient of dependent variable with respect to independent variable is called a differential equation.

Order of a differential equation: The order of a differential Equation is the order of the highest order derivative appearing in the equation.

For example, in the equation , the order of highest order derivative is 2. So. It is a differential equation of order 2.

The equation  is of the order 32, It is a differential equation of order 2.

Degree of a differential equation: The degree of a differential equation is the degree of the highest order derivative, when differential coefficient are made free from radicals and fractions.

Example I: Consider the differential equation

In this equation the number of highest order derivative is 2. So it is a differential equation of degree 1.

Example II: Consider the differential equation

In this equation, the order of the highest order derivative is 3. And its power its power is 2. So it is a differential equation of order 3 and degree 2.