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Getting Started with Differential Equations in Maple
September 2003
In this Maple session, we see some of the basic tools for working with differential equations in Maple.
We will only deal with first order equations here.
First, we need to load the "DEtools" library:
> with(DEtools):
Let's define a differential equation. As an example, we consider
y' = y(4-y).
This is a first order ordinary differential equation. (It is Problem 11 of Section 1.1 in the text.)
The following command defines a variable called "eq" that holds the differential equation:
> eq := diff(y(t),t) = y(t)*(4-y(t));
:= eq = ??t ( )y t ( )y t ( ) ? 4 ( )y t
A few points:
1. The derivative of y is specified with the "diff" command.
2. We can not drop the "(t)" from the dependent variable y. Maple treats "y" and "y(t)" differently,
and our equation is for "y(t)".
Two useful commands are "DEplot" and "dsolve".
Direction Fields with DEplot
Let's create a direction field for this equation. One Maple command t...

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