Find the degree of homogeneity of function $f (x, y) = x^{3} l n [\sqrt{x + y} / \sqrt{x - y}]$ .

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Solution

$f (x, y) = x^{3} ln (\frac{\sqrt{x + y}}{\sqrt{x - y}})$
$\Rightarrow f (t x, t y) = {(t x)}^{3} ln (\frac{\sqrt{t x + t y}}{\sqrt{t x - t y}}) = t^{3} x^{3} ln (\frac{\sqrt{x + y}}{\sqrt{x - y}}) = t^{3} f (x, y)$
Hence degree is $3$

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