 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-3/32c/c/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

For

f (x) = x^{- 2}

pr^{(3)} V_{2} (S - x^{- 2}) = - 2 S - x \frac{d}{d x} (x^{- 2}) = - 2 S + 2 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.

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