There is a smooth real-valued function f(x) defined on the positive reals such that, for all x>0 and for all y>0, the following identities are always true:(adsbygoogle = window.adsbygoogle || []).push({});

f(y) + 1/[(x^2)f(x)] = S/(xy)

f(x) – f(S) = y/(xS)

1/[(y^2)f(y)] - 1/[(S^2)f(S)] = x/(yS)

S is merely a function of x and y and is defined explicitly by the first equation.

It's easy to see that f(x)=1/x is one function that satisfies this system. Are there any other solutions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Professional Advice on Solving these Equations Would be Appreciated

**Physics Forums | Science Articles, Homework Help, Discussion**