1.08.4.Literacy - Growth Authors: Bill Davis, Horacio Porta...

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Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl ©1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 1.08 More Differential Equations LITERACY · L.1) Look at the differential equation y £ @ x D = y @ x D I 2 + Cos @ x D 2 - y @ x DM with y @ 0 D = 1. How do you know before you do any plotting that as x advances from 0, the plot of the solution y @ x D initially must go up? · L.2) Look at the differential equation y £ @ x D = y @ x D I 2 + Sin @ x D 2 - y @ x DM with y @ 0 D = 3. How do you know before you do any plotting that as x advances from 0, the plot of the solution y @ x D initially must go down? · L.3) Look at the differential equation y £ @ x D = y @ x D I 2 + Sin @ x D 2 - y @ x DM with y @ 0 D = 1. How do you know before you do any plotting that as x advances from 0, the plot of the solution y @ x D goes up near x's for which 2 + Sin @ x D 2 > y @ x D and the plot of the solution y @ x D goes down near x's for which 2 + Sin @ x D 2 < y @ x D ? Why do you expect that the crests and dips of the plot of y @ x D are located at places where the y @ x D plot crosses the plot of
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This note was uploaded on 10/11/2011 for the course MATH 241 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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