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How do I go about solving a differential equation of the form

[itex]\partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y)[/itex]

Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients in front of the derivatives which in this case are zero. If someone can point me in the right direction that could be great at least a way in which i can approach this. I am seeking an analytical solution

[itex]\partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y)[/itex]

Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients in front of the derivatives which in this case are zero. If someone can point me in the right direction that could be great at least a way in which i can approach this. I am seeking an analytical solution

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