(adsbygoogle = window.adsbygoogle || []).push({}); The ONLY solution of PDE: f_t g_r = f_r g_t ???

I have the following PDE:

[tex]\frac{\partial f(r,t)}{\partial t} \, \, \frac{\partial g(r,t)}{\partial r} = \frac{\partial f(r,t)}{\partial r} \, \, \frac{\partial g(r,t)}{\partial t}[/tex]

By a simple check, I know a solution is f = h(g), where h() is arbitrary function. The Maple PDE solver returns exactly that.

How can I prove, f=h(g) is the ONLY type of solution of that PDE?

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# The ONLY solution of PDE: f_t g_r = f_r g_t ?

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