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 d^{2}y/d^{2}t = - 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