A problem of a point source of $SH$-waves in a case of separation of the variables

The equation
$$ \operatorname{div}(\mu\nabla u)+\omega^2\rho u=-\delta(x-x_0)\delta(y-y_0), $$
where $\mu(x,y)=a(x)b(y)=a(x)b(y)(c(x)+d(y))$ ($a,b,c,d$ are given step functions) is considered. The problem is solved in explicit form and its asymptotic expansion, if $\omega\to0$, is found. Bibliography: 8 titles.