Question: Unique solution using pdsolve

Hi

I have a first oder PDE, I use pdsolve I obtained a solution depend on function F

condition_unique_solution.mw

 

My question: The boundary condition  f(x,y) = 1 is supplied on the line y = k x, where k is a constant. For which k
does there exist a unique solution for f(x, y)?

 

Many thanks for your help

 

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