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)

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