This may not be a very good question, but I'm totally stumped.
I need to know the power series representation of $x$, or if there even is one.
I'll show you why:
I am trying to solve $y''+2xy'-y=x$ using power series.
I know that $y''=\displaystyle\sum\limits_{n=2}^\infty a_n n(n-1)x^{n-2}$, $y'=\displaystyle\sum\limits_{n=1}^\infty a_n n x^{n-1}$, and $y=\displaystyle\sum\limits_{n=0}^\infty a_n x^n$, but I don't know what the power series representation of $x$ is.
I can solve the homogeneous equation no problem by setting $y''+2xy'-y=0$, but I do not feel this is correct.