Which of the following functions are homogene | vedclass

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(D) function $f(x, y)$ is homogeneous of degree $n$ if $f(\lambda x, \lambda y) = \lambda^n f(x, y)$.$A) f(x, y) = x \sin y + y \sin x$$f(\lambda x, \

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Both $(B)$ and $(C)$

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(D) function $f(x, y)$ is homogeneous of degree $n$ if $f(\lambda x, \lambda y) = \lambda^n f(x, y)$.$A) f(x, y) = x \sin y + y \sin x$$f(\lambda x, \lambda y) = \lambda x \sin(\lambda y) + \lambda y \sin(\lambda x) = \lambda(x \sin(\lambda y) + y \sin(\lambda x))$.Since this is not equal to $\lambda^n f(x, y)$,it is not homogeneous.$B) f(x, y) = x e^{y/x} + y e^{x/y}$$f(\lambda x, \lambda y) = \lambda x e^{\lambda y / \lambda x} + \lambda y e^{\lambda x / \lambda y} = \lambda(x e^{y/x} + y e^{x/y}) = \lambda^1 f(x, y)$.This is a homogeneous function of degree $1$.$C) f(x, y) = x^2 - xy$$f(\lambda x, \lambda y) = (\lambda x)^2 - (\lambda x)(\lambda y) = \lambda^2 x^2 - \lambda^2 xy = \lambda^2(x^2 - xy) = \lambda^2 f(x, y)$.This is a homogeneous function of degree $2$.Therefore,both $(B)$ and $(C)$ are homogeneous functions.

Which of the following functions are homogeneous?

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