HOMOGENEOUS FUNCTION

Students often don't understand the difference between ordinary function and homogeneous. It is not a difficult thing. A function is homogeneous if the sum of powers of variables of each term of that function is same.

In the picture above the sum of the powers of variables of each term of the first function is same and is 3. So the first function is homogeneous. But the other two functions do not fulfill the condition.We can figure out homogeneous functions by this way easily. But all the time this rule do not satisfy. So more formal way is needed to figure out homogeneous functions that is: a function f(x,y) homogeneous if

or

From the picturesabove we can understand that the function f(x,y) is a homogeneous function of power n.