I am not sure again, whether this belongs here or in mathematics. When we have a partial differential equation, in general we can write the solution of [itex]F(r,t)[/itex] as: [itex]F(r,t)=R(r)T(t)[/itex] In the procedure of separating the differential equation, we find ourselves dividing with [itex]F(r,t)[/itex]. Isn't that actually problematic for points where [itex]R[/itex] or [itex]T[/itex] happen to be zero? I know that they can't be zero everywhere coz the solution would be trivial, but what stops them from being zero at distinct points? Actually nothing... The only solution to this problem would be the imposing of continuity at the point of interest, setting the left side solution equal to the right side. But dividing with zero is still a problem :( Thanks.