The following problem comes from the section Separable Differential Equations in a traditional calculus text. It requires no more than a separation of variables and an “integration of both sides” to produce the solution of the differential equation in an implicit form. However, we show that additional insight is possible if we ask questions like “How does the solution behave?” and “What is the nature of the implicit function describing the solution?” The role of Maple in answering these questions is essential.
KeywordsAsymptotic Behavior Asymptotic Expansion Taylor Series Additional Insight Real Solution
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