Concept explainers
Increasing and decreasing solutions Consider the following differential equations. A detailed direction field is not needed.
a. Find the solutions that are constant, for all t ≥ 0 (the equilibrium solutions).
b. In what regions are solutions increasing? Decreasing?
c. Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing?
d. Sketch the direction field and verify that it is consistent with parts (a)–(c).
20. y′(t) = y(y + 3)(4 – y)
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