= Solution
Let $L=d^2/dx^2+x^{-1}d/dx-x^{-2}$. A <Green's function> $G(x,\xi)$ satisfies $L_xG=\delta(x-\xi)$ and the chosen homogeneous <boundary conditions> in $x$. Away from $x=\xi$, it is a linear combination of $x$ and $x^{-1}$. It must be continuous there and obey the unit derivative jump $G_x(\xi^+,\xi)-G_x(\xi^-,\xi)=1$, because the leading differential coefficient is one. Then
$$
y(x)=\int_0^\infty G(x,\xi)f(\xi)\,d\xi
$$
solves $Ly=f$ whenever the integral and boundary limits are valid. The <Wronskian> of $x,x^{-1}$ is $-2/x$. The <Green kernels for a radial dipole Euler equation> implement the two different choices of boundary conditions below.
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