Question: Find two vector fields (i,y) = (P.(x,y), Q1(x, y)) and (i,y) = (P2(x,y), Q2(x, y)) and two functions F1(x,y), F2(x, y) such that each function

Find two vector fields (i,y) = (P.(x,y), Q1(x, y)) and (i,y) = (P2(x,y), Q2(x, y)) and two functions F1(x,y), F2(x, y) such that each function is a first integral of the corresponding vector field but their sum is not the first integral of the vector field (d, y) = (P2(x, y) + P2(+,y), Q.(x, y) +Q2(x, y)).

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