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I would like to find some functions F(x,y) which satisfy the following equation

[itex]

\frac{F(x,y)}{\partial x}=\frac{F(y,x)}{\partial y}

[/itex]

For example this is obviously satisfied for the function

[itex]

F= exp(x+y)

[/itex]

I would like however to find the most general closed form solution.

Do you have any ideas?

Could it be that it has to be a function of x+y only for example?

I tried to get some info by taylor expantions but I was not so succesful.

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# What can we say about the solution of this PDE?

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