Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 3 / 10A / b / i / Solution

For radial functions, ${\nabla }^{2}h=h^{\prime \prime }+2h^{\prime }/r$. Since ${\nabla }^2{e}^{-r}=e^{-r}-2e^{-r}/r$ and ${\nabla }^2{r}^{-4}=12r^{-6}$, decay and the boundary value give

Solved by gpt-5.6-sol high.