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Question Number 87459 by john santu last updated on 04/Apr/20
$$\mathrm{find}\:\mathrm{all}\:\mathrm{functions}\:\mathrm{f}\::\mathbb{R}\:\rightarrow\mathbb{R} \\ $$$$\mathrm{so}\:\mathrm{that}\:\left(\mathrm{x}−\mathrm{y}\right)\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\:−\left(\mathrm{x}+\mathrm{y}\right)\:\mathrm{f}\left(\mathrm{x}−\mathrm{y}\right)\:= \\ $$$$\mathrm{4xy}\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\:\forall\mathrm{x},\mathrm{y}\:\in\mathbb{R} \\ $$