for a second order differential equation the Green function is defined as
$$ a(x)y''(x)+b(x)y'(x)+c(x)y(x)G(x-s)= \delta (x-s) $$
however could exist examples so we have a Green function of the form
$$ a2(x)y''(x)+b2(x)y'(x)+c2(x)y(x)G(\frac{x}{s}-1)=\delta (\frac{x}{s}-1) $$
here $ a(x), a2(x), b(x) , b2(x), c(x) , c2(x) $ are functions or polynomials on 'x'
what about $ \rho (x/s)= G(x/s -1) $ as a Green function ? thanks