Function

Relation: If A and B are two non empty sets, then A cross B is a set and the subset of A cross B is called relation.

Function:If a belongs to A and b and b' belong to B and (a,b) and (a,b') belong to A cross b then it(A cross B) is a function if b=b'. That means function is a kind of relation where two ordered pair would not have same first element in its pairs but a function can have same second element.
That means if (a,b) and (a',b) both belong to A cross B then A cross B could be said as a function.
f={ (0,1) , (55,22), (3,-50) }
g={ (2, 1) , (5, 2), (2, 9) }
h={ (1,7) , (1, 7), (33, 7), (32, 7) }
Here f, g and h are three relations. But f is a function and others are not

For help: http://www.mathwarehouse.com/algebra/relation/math-function.php

Order And Degree

A differential equation is an equation which involves derivatives is called a differential equation.

Order: The highest power of a differential equation is called its order.

Degree: Dimension of the highest power of a differential equation is called its degree.

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.