section2-2.mws

Assignment 1

Section 2.2

9/11/00

Richard Hitt

Introduction

Here is one way of solving the exercises from section 2.2 in the text.

Getting started

Every Maple worksheet should begin by re-initializing the Maple "kernel" and loading the additional packages that we are most likely to use.

> restart;

> with( plots ):

> with( DEtools ): 

Warning, the name changecoords has been redefined

Problem 2(e) on page 32

First we solve the DE exactly using dsolve.

> de1 := diff(y(x),x) - tan(x)*y(x) = 6;

de1 := diff(y(x),x)-tan(x)*y(x) = 6

> dsolve(de1, y(x));

y(x) = (6*sin(x)+_C1)/cos(x)

Next, we can plot several typical solutions.

> DEplot( de1, y(x), x=0..Pi, y=-3..3, [[0,-3],[.6,-3],[.8,-3],[1.7,3],[2,-3],[2.7,-3]], stepsize=.01, linecolor=blue );

[Maple Plot]

>

Problem 2(i) on page 32

Again, we solve the DE exactly.

> de2 := (x-5)*(x*diff(y(x),x)+3*y(x))=2;

de2 := (x-5)*(x*diff(y(x),x)+3*y(x)) = 2

> dsolve(de2, y(x));

y(x) = (x^2+10*x+50*ln(x-5)+_C1)/(x^3)

Then we plot typical solutions.

> DEplot(de2, y(x), x=5.1..8, y=-5..5, [[5.1,-4],[5.1,-3],[5.1,-2],[5.1,-1],[5.1,0],[5.1,1],[5.1,2],[5.1,3],[5.1,4]], linecolor=blue);

[Maple Plot]

>