When using the Frobenius method of solving differential equations using power series solutions, I get a solution y = (indicial_stuff) + (infinite_summation_stuff) = 0 for a differential equation differential_stuff = 0. WHY is it that I can say (indicial_stuff) = 0? If y = (indicial_stuff) * (infinite_summation_stuff) = 0 (NOTICE THE MULTIPLICATION INSTEAD OF ADDITION) then it would make sense to me that (indicial_stuff) = 0 but with the addition, I cannot make sense of this. I tried to generalize this question and hope that I haven't made it more confusing but, if I have made the question confusing, please tell me and I will clear things up as best as I can. Basically, I'm just asking for the reason why this – the isolation of the indicial polynomial equation (and the other summation portion) - is justified. Any input would be greatly appreciated! Thanks in advance!