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Lecture Notes for MATH 308 - Differential Equations at Colgate (CU)

Notes Information

Material Type:Class Note
Professor:Staff
Class:MATH 308 - Differential Equations
Subject:Mathematics
University:Colgate University
Term:Fall 2003
Keywords:
  • Plot Command
  • Square Brackets
  • Unfortunately
  • Initial Condition
  • Approximations
  • Solution Curve
  • Dependent Variable
  • Initial Conditions
  • Right Hand Side
  • Right-Hand Side
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Sample Document Text

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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