Consider the autonomous DE Use your ideas from Problem 35 to find intervals on the y-axis for which solution curves are concave up and intervals for which solution curves are concave down. Discuss why each solution curve of an initial-value problem of the form where -2 < y0 < 3, has a point of inflection with the same y coordinate. What is that y-coordinate? Carefully sketch the solution curve for which y(0)=-1. Repeat for y(2) = 2
(reference problem 35)
Using the autonomous equation (2), discuss how it is possible to obtain information about the location of points of inflection of a solution curve.
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