I have a question about existence and uniqueness. It says that if f(x,y)=dy/dx and partialf/partialy are both continuous on the xy plane, then there is one and ony one solution etc... My question is, how can you tell if the function f and the partial derivative are continuous on the xy plane if they aren't even functions in the xy plane. They are functions in 3 space. You cannot even graph dy/dx= f(x,y). For instance, if dy/dx== 2y/x, that is not in the xy plane. That is a function of 2 variables in 3 space. I am confused?

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