how can i solve $ -ixDG(x,s)-iG(x,s)/2= \delta ( \frac{x}{s}-1) $

i do not know , since it is a first odrder differntial operator, the formal solution i've found would be

$ G(x,s)= \sum_{n} \frac{u_{n}(x)u_{m}(s)}{\lambda _{n}} $

where $ -ixDu_{n}(x)-iu_{n}(x)/2= u_{n} \lambda _{n} $

here G(x,s) is the analogue of the Green function for our operator :)