Find all function $f:\mathbb{R}\rightarrow \mathbb{R}$ such that $f(x+y)-2f(x-y)+f(x)-2f(y)=y-2,\forall x,y\in \mathbb{R}$.
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Tags: algebra, functional equation
Find all function $f:\mathbb{R}\rightarrow \mathbb{R}$ such that $f(x+y)-2f(x-y)+f(x)-2f(y)=y-2,\forall x,y\in \mathbb{R}$.