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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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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