So there are several ways of finding general positive solutions for the equation $x^y=y^x$. But does this equation appear anywhere in physics or other science ? Or maybe there is some practical purpose for it. Thanks in advance.
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1For an overview and some applications, consult this paper by Knoebel (http://eretrandre.org/rb/files/Knoebel1981_158.pdf). – Sep 19 '18 at 21:54
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The solution is essentially given by the Lambert W function, for which you can find a list of applications on Wikipedia:
https://en.wikipedia.org/wiki/Lambert_W_function#Applications
Does this help?
zakk
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2Websites can go down, and that Wikipedia page might be restructured considerably at some point. Can we add a few bullet points? – Bladewood Sep 19 '18 at 20:51
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It is more about Lambert W function than the equation itself, but still thanks. – Юрій Ярош Sep 19 '18 at 21:09