Which of the following is not a homogeneous f | vedclass

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(D) function $f(x, y)$ is said to be a homogeneous function of degree $n$ if $f(\lambda x, \lambda y) = \lambda^n f(x, y)$.$1$. For $f(x, y) = y^2+2xy

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$\cos x+\sin y$

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(D) function $f(x, y)$ is said to be a homogeneous function of degree $n$ if $f(\lambda x, \lambda y) = \lambda^n f(x, y)$.$1$. For $f(x, y) = y^2+2xy$,$f(\lambda x, \lambda y) = (\lambda y)^2 + 2(\lambda x)(\lambda y) = \lambda^2(y^2+2xy) = \lambda^2 f(x, y)$. This is homogeneous of degree $2$.$2$. For $f(x, y) = 2x-3y$,$f(\lambda x, \lambda y) = 2(\lambda x) - 3(\lambda y) = \lambda(2x-3y) = \lambda^1 f(x, y)$. This is homogeneous of degree $1$.$3$. For $f(x, y) = \sin\left(\frac{y}{x}\right)$,$f(\lambda x, \lambda y) = \sin\left(\frac{\lambda y}{\lambda x}\right) = \sin\left(\frac{y}{x}\right) = \lambda^0 f(x, y)$. This is homogeneous of degree $0$.$4$. For $f(x, y) = \cos x + \sin y$,$f(\lambda x, \lambda y) = \cos(\lambda x) + \sin(\lambda y)$. This cannot be expressed in the form $\lambda^n f(x, y)$ for any $n$.Therefore,$\cos x + \sin y$ is not a homogeneous function.

Which of the following is not a homogeneous function?

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