Dear all, I have posted this question on m.s.e. Unfortunately, no one responded to answer. I hope, this site and members of this site will answer my questions.

The equation $x^n - ny^x-nxy$ = $0$ has solution set $(n, x, y) = (1, 1, \frac12), (2, 1, \frac14), (3, 1, \frac16), \ldots$

I would like to know/learn the following (Kindly discuss)

1) If we want to know the graph. How would be the look of the graph and what kind of graph we get?

2) The cited above equations has infinite solutions with $x = 1$. Can we have solutions with $x >1$ and other $n, y$ are some positives?

3) If solutions exists how to find them for $x < 1$ and $x > 1$?

Thanks in advance.

integeralsolutionsonly. Now you mention solutions containing rational numbers. It is now not clear what exactly you are looking for. Please clarify. $\endgroup$ – user9072 Feb 12 '13 at 12:34