Assignment 3

Section 3.4

9/25/00

Richard Hitt

Introduction

Here are solutions to the exercises from section 3.4 that were turned in.

Getting started

> restart;

> with( plots ):

> with( DEtools ):

Warning, the name changecoords has been redefined

In Maple 6, you can turn on deeper levels of reporting on what Maple does as it solves a DE with the following command:

> infolevel[dsolve] := 3;

Problem 4(j) on page 108

First we solve the DE exactly using dsolve.

> de1 := diff(y(x),x$2) + 2*diff(y(x),x) + 3*y(x) = 0;

> dsolve(de1);

The above command produced the general solution. For the particular solution in the problem we do

> sol:=dsolve({de1,y(0)=0,D(y)(0)=3},y(x));

Then to plot it, we can grap the right-hand-side of the solution and give it to the plot command.

> plot(rhs(sol),x=-3..2);

>

Problem 4(n) on page 108

Again, we solve the DE exactly.

> de2 := diff(y(x),x$4)-y(x)=0;

> dsolve(de2);

Problem 6(j) on page 108

> de3:=diff(y(x),x$4)+8*diff(y(x),x$2)+16*y(x)=0;

>

> dsolve(de3);

>