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Does the existence and uniqueness theorem apply to the

1. Does the existence and uniqueness theorem apply to the differential equation y' = |y|?

2. Consider y'= y2 - A, where A is a parameter. Find all equilibrium points and determine their type (your answer will, of course, depend on A).

3. Consider y' = Ay(1 - y), where A is a parameter. Find all equilibrium points and determine their type.

4. What is the actual behavior of solutions of y' = 1+ y ? 1- y

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Microeconomics: Does the existence and uniqueness theorem apply to the

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