In bucolic farm there a contagion spreading among 500 happy cows, some with spots others with- out. There are no other breeds of cows in the field. The contagion spreads through contact. Cows without spots that come in to contact with cows with spots immediately develop spots. Assume that during the modeling period the effects are immediate and permanent (spotted cows remain spotted). It is reasonable to assume that the rate at which cows develop spots is proportional to the product of the number of spotted cows and the number of non-spotted cows. Let S = S(t) be the number of spotted cows at time t. Write a differential equation reflecting the situation.

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