[oKiNeSIuMo]

$(x-y)f(x+y)-(x+y)f(x-y)=4xy(x^2-y^2)$
$\frac{f(x+y)}{x+y}-\frac{f(x-y)}{x-y}=4xy=(x+y)^2-(x-y)^2$
$\frac{f(x+y)}{x+y}-(x+y)^2=\frac{f(x-y)}{x-y}-(x-y)^2$
$\therefore \frac{f(x)}{x}-x^2=c$
$\therefore f(x)=x^3+cx$