How do I solve a PDE with a Dirac Delta function? @user12477 I didn't knew the distributional rule you mentioned, it might be useful in my reaserch :). Still, I don't believe that just apply this formula is a constructive answer, specially when there are edgy details in the application. The formula relies entirely on the existence and uniqueness of the solution of the equivalent system of ODEs, and it might be clear for you that it can be extended to this case, but it's certainly not trivial.