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Question A 04
Which differential equation below is the appropriate one for the slope field shown in the figure?
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How to relate direction field to differential equation?
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First we observe there are two steady states (where y’=0) and . Then from the direction of those vectors, we find is unstable and is stable for , unstable for . To obtain the correct stability of those steady states, we must have
The first observation eliminates options a) and d). The third observation rules out option b). Option e) is not valid because a steady state must exist when . Thus the only possible answer is (c).