Find the solution $Y \in \mathbb{R}^\mathbb{R}$ of difference equation $y(x+2) - y(x+1) + 2y(x) = x$ on $\mathbb{R}$ such that $\forall x \in [0,2): Y(x) =x$
This is all the information of the given question that I am trying to solve.
I need some help/guidance to help me solve this question and understand the solving mechanism of difference equations.
Thank you all.
Hint: try getting rid of the $x$ by putting $g(x)+tx=y(x)$.