Question

homogeneous equation with examples

Answer 1

solution is a homogeneous mixture
ex- solution of salt and water

Answer 2

A function f( x,y) is said to be homogeneous of degree n if the equation


   


holds for all x,y, and z (for which both sides are defined).


Example 1: The function f( x,y) = x 2 + y 2 is homogeneous of degree 2, since


  



Example 2: The function  is homogeneous of degree 4, since 






Example 3: The function f( x,y) = 2 x + y is homogeneous of degree 1, since 






Example 4: The function f( x,y) = x 3 – y 2 is not homogeneous, since 


 


which does not equal z n f( x,y) for any n.

Example 5: The function f( x,y) = x 3 sin ( y/x) is homogeneous of degree 3, since