Module 20  Antiderivatives as Indefinite Integrals and Differential Equations  
Introduction  Lesson 1  Lesson 2  Lesson 3  Lesson 4  SelfTest  
Lesson 20.3: Solving Differential Equations Numerically  
In this lesson you will use the TI83 program EULERT to make tables for solutions to initial value problems. Downloading the Program to Your Computer
Transferring the Program to the TI83 If necessary, click here to get information about how to obtain the needed cable and review the procedure to transfer the program from your computer to your calculator. EULERT Entries The entries for EULERT are similar to EULERG. You enter the differential equation in Y_{1}. When you run EULERT you will see prompts for the initial values of X and Y as well as the step size. When running EULERT, you also need to enter the number of points to be computed. When EULERT runs, instead of seeing a graph, you will see approximate coordinates of points on the graph of the solution. Numerical Solutions to Differential Equations EULERT also uses Euler's method, and therefore only gives approximate numerical solutions. Find a numerical solution to the initial value problem y' = 2x with the condition that y(0) = 1 by using EULERT.
After you enter the number of points you should see the coordinates for the initial point. The busy indicator should appear in the upper righthand corner of the screen. Each time you press you will see another pair of coordinates. These coordinates are approximations of points on the solution curve.
This result says that the point (1,1.9) lies on the graph of the solution to the initial value problem y' = 2x, y(0) = 1. Approximate Answers from EULERT The analytic solution to the initial value problem is y = x^{2} + 1. In the solution when x = 1, y = 2, yet with a step size of 0.1 the program predicted a yvalue of 1.9. EULERT uses a numerical method that gives approximate, not exact solutions to initial value problems. 20.3.1 Redo the same problem above with a step size of 0.05 to see which value for y is predicted by the program for x = 1. Click here for the answer.
20.3.2 Given and y(1) = 1 use EULERT to estimate y(1.2). Use a step size of 0.05. Click here for the answer. 

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