Class 12 Maths Differential Equations Homogeneous Function

Homogeneous Function

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

F(λx, λy) = λn F(x, y) for any nonzero constant λ.

Eg:    F(x, y) = y2 + 2xy    

F(λx, λy) = (λy)2 + 2λxλy

F(λx, λy) = λ2 (y2 + 2xy )  

Thus, F(x, y) = y2 + 2xy      is  a homogeneous function.


But,  F(x, y) = sin x + cos y is not a homogeneous function since it cannot be expressed as F(λx, λy) = λn F(x, y)

Share these Notes with your friends  

< Prev Next >

You can check our 5-step learning process