# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of Integral, Antiderivatives and Definite Integrals

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• ##### Other Materials
This is Activity 7 from the EXPLORATIONS Book:
Advanced Placement Calculus with the TI-89.

## Differential Equations and Slope Fields - Activity 7

#### Activity Overview

In this activity, students investigate the use of the differential equation graphing mode to solve various differential equations. They learn and explore to use numerical and graphical methods for solving various differential equations.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 59 - 68 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

Slope Fields and Specific Solutions:

• Enter differential equation and graph the solution in the Zoom Decimal window
• Graph the family of solutions and trace the specific solution to the differential equation

• Window Variables and Initial Conditions:
• Enter the differential equation and graph the solution, using appropriate window variables and initial conditions

• Tabular Solutions to differential equations:
• Enter the differential equation and set the table parameters
• Use Runge-Kutta or Euler method to find the solution

• Higher-order Differential Equations:
• Graph the solution to the equation
• Use the Differential Equation solver to find an analytical solution

• Modeling Baseball Trajectories:
• Enter the equations
• Specify the x and y axes and graph the solution
• #### After the Activity

Students will complete the practice exercise problems.
Review student results:

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