When you say “which yields a solution of the form f(w)=c1/(1−w)+c2”, are you saying that f′(w)/f(w)=1/(1−w) yields that, or are you saying that (1−w)f′(w)−f(w)>0 yields that? Because, for the former, that seems wrong? Specifically, the former should yield only things of the form f(w)=c1/(1−w) .
I meant the former (which you’re right only has the solution with c1). I only added the c2 term to make it work for the inequality. As a result, it’s only a subset of the solutions for the inequality. The (quite complicated!) expression you provided also works.
I meant the former (which you’re right only has the solution with c1). I only added the c2 term to make it work for the inequality. As a result, it’s only a subset of the solutions for the inequality. The (quite complicated!) expression you provided also works.