Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 32C / c / iii / Solution

For $f(x)=x^{-2}$,which vanishes when $S=x^{-2}$. The corresponding expressions for $V_1$ and $V_3$ are nonzero on the equation. Thus $S[u]=x^{-2}$ has the dilation symmetry $V_2=x{\partial }_x$ among the three listed generators.