Thanks for the answer. I totally agree but let me explain better. My problem indeed is to solve

so it is the function u that has a maximum at u=1. It is part of a model with a negative feedback of u on itself. so what I am trying to find here is the time for the maximum. The straight answer is that it is infinite, but my question is: is there any other possibility, as for example, a branch point in u(t)? I can solve it using a numerical method but I need to do it analytically.

Thanks for any help.