Education Technology

Higher Order Differential Equations

Activity Overview

In this activity, students use the calculator to graph the solution to a second-order and third-order differential equations. They convert higher order differential equations by substitution to a system of first order differential equations.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 27 - 34 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.
    Follow the Activity procedures:
    Acceleration Due to Gravity:

  • For a ball dropped from a height of 2 meters, velocity is dy/dt and acceleration is d2y/d2t = - 9.8
  • Reduce the second-order equation by substitution to a system of first-order equations
  • Enter both the primary and the substituted differential equation on the calculator
  • Set different styles for graphing both the differential equations and graph the equations
  • Use the trace function on the graph and record the time when a ball will hit the ground
  • Record the value of the acceleration when the ball hits the ground

  • Third Order Differential equation:
  • Reduce the third-order differential equation to a system of first-order differential equations and enter it on the calculator
  • Select the initial conditions, window viewing parameters, and graphing parameters
  • Graph the solution to the differential equation
  • Enter the analytic solution and compare it to the graphed solution

  • LRC Circuits:
  • Reduce the second-order differential equation for calculating electromotive force in a circuit to a first-order differential equation and enter it on the calculator
  • Find numeric solutions and generate a table of values for the second-order differential equation
  • Set the point of start and ending point of the graph to an appropriate range
  • Change the values of the viewing window and graph the equations
  • Observe the connection between the graph and the table of values
  • After the Activity

    Students complete the problems on the exercise page.
    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary