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Two chemical solutions, one containing N molecules of chemical A and another containing M molecules of chemical B, are mixed together at time t = 0. The molecules from the two chemicals combine to form another chemical solution containing y (AB) molecules. The rate at which the AB molecules are formed, , is called the reaction rate and is jointly proportional to
and
. Thus,
where k is a constant (we assume the temperature of the chemical mixture remains constant during the interaction). Solve this differential equation with the side condition
assuming that
and
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