Theorem:

Suppose that in an open disk the following equation holds [Maple Math] where [Maple Math] are functions obtained by differentiating [Maple Math] with respect to [Maple Math] for [Maple Math] and with respect to [Maple Math] for [Maple Math] while [Maple Math] is continuous function obtained by first differentiating [Maple Math] with respect to [Maple Math] , and then with respect to [Maple Math] . (Note if [Maple Math] is continuous, then [Maple Math] so the order of differentiation does not matter.) Then [Maple Math] is sepearable.

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