# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of the Derivative

• ##### Author 9-12

60 Minutes

• TI-86
• ##### Other Materials
This is Activity 3 from the EXPLORATIONS Book:
Differential Equations With The TI-86

## 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.
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