Concept explainers
In Problems 15–18 verify that the indicated function y = ϕ(x) is an explicit solution of the given first-order differential equation. Proceed as in Example 6, by considering ϕ simply as a function and give its domain. Then by considering ϕ as a solution of the differential equation, give at least one interval I of definition.
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Chapter 1 Solutions
First Course in Differential Equations (Instructor's)
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- From its past behavior, John knows that the value of a stock has a cyclical component that increases for the first three months of each year, falls for the next six, and rises again for the last three. In addition, inflation adds a linear component to the stock's price. John is seeking a model of the form f(t) = mt + b + A sin (-) with t in months since Jan 1. He has the following data in the table: Jan 1 Apr 1 Oct 1 Jan 1 Date Jul 1 Price $20.00 $37.50 $35.00 $32.50 $50.00 a) What is the length of the period in his model? b) Determine two months when the Price is on the slanted midline. c) Find value ofm, b, and A so that f fits the data.arrow_forward1. Show that the given functions are solutions of the given differential equation?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,