Solution
= Solution
The <Dirichlet boundary condition> gives $B=-a^2/6$, so the unique radial solution is
$$
\boxed{u(r)=\frac{r^2-a^2}{6}.}
$$
Its <radial Laplacian> is one, it is smooth at the origin, and its boundary value is zero. The uniqueness result in part (i) shows that this is also the only solution among all classical <functions> on the ball, not merely among spherically symmetric ones.