I am trying to find the dimension of the vector space ($P_2$ means polynomials of degree at most $2$) $V = \{p(x) \in P_2 \mid xp'(x) = p(x)\}.$ However, I don't even know how to start...
(Additionally, the question asks to find the basis for $V$, which I don't know how to do, but I think I might if someone tells me how to understand the above first...)