I'm investigating the solution of the special case of the Bernoulli differential equation $$ \dfrac{dy}{dt} = \dfrac{y(1-y)}{\tau}, \tag{1} $$ with $\tau$ a time constant, and which models innovation processes fairly well, and whose solution is the logistic curve $$ y = \dfrac{1}{1+e^{-t/\tau}}.\...

Solve the equation $$x+\sqrt{x+\frac12+\sqrt{x+\frac14}}=4$$ Actually I have solved this question but I want to know other methods of solving this question. It's not that I am curious for just elementary methods but you all can give solutions using advance maths too (which I'll see and learn). ...

Solve the equation $$x+\sqrt{x+\frac12+\sqrt{x+\frac14}}=4$$ Actually I have solved this question but I want to know other methods of solving this question. It's not that I am curious for just elementary methods but you all can give solutions using advance maths too (which I'll see and learn). ...

I propose to create this tag : alternate-solution for my most recent question. This tag is to be used when the user is asking different approaches for the same question. Is there such a tag existing already? If not, can I proceed to create this?

I am against the creation of such a tag. It would be a "meta tag" and for the most part we try to avoid those. The information that you are searching for an alternative solution should be conveyed in the body of the post.

Consider the well-known categorical result: Theorem 1.5.9 (of Riehl's book). A functor defining an equivalence of categories is full, faithful, and essentially surjective on objects. Assuming the axiom of choice, any functor with these properties defines an equivalence of categories. I was wond...