Math 2650 - Qualatative Analysis Direction Fields A. J. Meir Copyright (C) A. J. Meir. All rights reserved. This worksheet is for educational use only. No part of this publication may be reproduced or transmitted for profit in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system without prior written permission from the author. Not for profit distribution of the software is allowed without prior written permission, providing that the worksheet is not modified in any way and full credit to the author is acknowledged.

One of the emphases of the class is qualitative analysis. This is important since most differential equations cannot be solved explicitly, although in many cases we can still say someting about the solution to the equation (existence, uniqueness, and qualatative behavior). Even thogh we may not be able to find an explicit representation for the solution we may be able to show the solution exists and that it is unique, furthermore we may be able to answer the questions: Does the solution tend to 0 or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJmluZmluO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn tends to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJmluZmluO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn? Is the solution periodic, and if so with what period? Does the solution approach 0 , or some other value only as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn tends to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJmluZmluO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn, or for some finite time LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn? Does the solution "converege" to some other function as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn tends to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJmluZmluO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn?

Starting the DE tools. The basic Maple command for the graphical representation of direction fields and approximate solution curves is DEplot ; it is part of a package of routines called DEtools, which must be explicitly loaded with the command. with(DEtools):

The direction field is comprised of slope lines of the differential equation, for example, 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 then 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 is the slope of the graph of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJ0RidGNEY3LyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0Y+Rj5GZm5GPkYrRmZuRj4= the solution at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn. A solution of the differential equation is a function whose graph is consistent with the direction field (that is the tangent to the graph at each point must coincide with the slope line at that point). Isoclines are curves along which the slope lines have constant slope (they are given by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUkobWZlbmNlZEdGJDYkLUYjNictRiw2JVEidEYnRjZGOS1GPTYtUSIsRidGQEZCL0ZGRjhGR0ZJRktGTUZPRlEvRlVRLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRjZGOS8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRidGQEZARmFvRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1GLDYlUSJjRidGNkY5RmFvRkBGK0Zhb0ZA, that is isoclines are level curves of the function f).

Some examples

We will set k=1. k:=1: DEplot(D(x)(t)=k*x(t),x(t),t=-4..4,x=-4..4);

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For 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, then LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn is increasing. For 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, then LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn is decreasing. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn cannot change sign. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj4vJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnRj5GK0ZYRj4= is a constant solution (corresponding to the initial condition 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), it is the only constatnt solution. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn does not approach a constant value as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn tends to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJmluZmluO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjNRJ25vcm1hbEYn.

DEplot(D(x)(t)=k*x(t),x(t),t=-4..4,x=-4..4, {[x(0)=-1],[x(0)=0],[x(0)=1]});

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