Exercise (Based on Homogeneous Functions)
An expression of the form in which every term is of the nth degree, is called homogenous function of degree n, which can be also written as
This function further can be expressed in the form of is called homogeneous function of degree n in and . For example is a homogeneous function of degree 4 in and . In general, a function is said to be homogeneous function of degree n in , if every term containing these variable combines to give degree of n, therefore can be expressed in the form .
Euler’s theorem of homogeneous functions
If u be a homogeneous function of degree n in and , than
Since u is a homogeneous functions of degree n in and y, therefore
So, in general, if u is a homogeneous function of degree n in then
Above expression represents the general form of Euler’s Theorem.