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Text from Homogeneous Functions article One can specialise the theorem to the case of a function of a single real variable (n = 1), in which case the function satisfies the ordinary differential equation
 * $$ f'(x) - \frac{k}{x} f(x) = 0$$.

This equation may be solved using an integrating factor approach, with solution $$\textstyle f(x) = c x^k$$ for some constant real number c.