TI-89 Graphing Calculator: Solving Initial Value Problems

This tutorial demonstrates how to solve first-order initial value problems using the TI-89 graphing calculator. It covers the use of the desolve function under the calculus menu to solve differential equations with initial conditions. The tutorial provides step-by-step instructions for entering equations and conditions, and it includes examples with different independent variables. The video concludes with a summary of the solutions obtained.

What is the primary function used on the TI-89 calculator to solve initial value problems?

• Integral

• Graph

• Derivative

• deSolve

Which menu option is used to access the deSolve function on the TI-89?

• Option A

• Option B

• Option C

• Option D

What is the initial condition for the first differential equation y' = 2x?

• y(3) = 5

• y(2) = 4

• y(1) = 3

• y(0) = 1

What is the particular solution for the differential equation y' = 2x with y(1) = 3?

• y = x^2 + 3

• y = x^2 + 2

• y = x^2 + 4

• y = x^2 + 1

How should y ln(x) be entered in the TI-89 for the second differential equation?

• y + ln(x)

• y * ln(x)

• y / ln(x)

• y - ln(x)

What is the initial condition for the second differential equation y' = y * ln(x)?

• y(2) = 3

• y(1) = 2

• y(3) = 4

• y(0) = 1

What is the solution for the differential equation y' = y * ln(x) with y(1) = 2?

• y = 2 * x^2 * e^(x-1)

• y = 2 * x^2 * e^(1-x)

• y = 2 * x^x * e^(x-1)

• y = 2 * x^x * e^(1-x)

In the third example, what is the independent variable?

• y

• x

• z

• t

What is the initial condition for the third differential equation with t as the independent variable?

• y(2) = 1

• y(3) = 2

• y(0) = 1

• y(1) = 2

What is the particular solution for the third differential equation?

• y = 2 + sin(t) - sin(2) / t

• y = 2 + cos(t) - cos(2) / t

• y = 2 + sin(2) - sin(t) / t

• y = 2 + cos(2) - cos(t) / t