Integration of Two Variable Function?
My honest opinion: I fail to see any new concept, I think you are just abusing notation. First you define $f'(x,y) = 3x^2+y$ and then you identify $f'(x,y) = dy/dx$. There is no two-variable function, you are just solving the ordinary differential equation $f'(x) = 3x^2+f(x)$ with weird notation.