Concept explainers
Direction fields Consider the direction field for the equation y′ = y(2 – y) shown in the figure and initial conditions of the form y(0) = A.
a. Sketch a solution on the direction field with the initial condition y(0) = 1.
b. Sketch a solution on the direction field with the initial condition y(0) = 3.
c. For what values of A are the corresponding solutions increasing, for t ≥ 0?
d. For what values of A are the corresponding solutions decreasing, for t ≥ 0?
e. Identify the equilibrium solutions for the differential equation.
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