\(\displaystyle \frac{\partial F}{\partial x} + \frac{\partial F}{\partial y} = 0\)

I have manged to find out that \(\displaystyle F = f(x - y)\) satisfies the above when \(\displaystyle f\) is continues and differentiable everywhere on the xy plane.

Is it possible to show that there are no more class of solutions to this one? Even if the RHS is is different in the given PDE, it seems AFAIHO, that the solution is dependent on this particular form.

Thanks in advance,

Balarka

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