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