I think that this problem is given in a context that deals with the Gompertz differential equation. You have not provided this equation, so it is not clear a solution to what is being discussed.
I have no idea what this question is asking me:
27. Show that is a solution for any constant a.
it gives me this hint:
dy/dt = ky ln(y/m).
I would assume that because it is an exponent that any constant for a would give a definable solution.
I do not know what it is I am trying to prove or what is going on, any help would be appreciated.