Name:__________________________________________________________

You may work in-groups of 2 or 3 on this project. Please complete and turn in a separate copy for each of you though.

Part 1: The Tutorial

We can graph the slope fields for a differential equation, and by specifying an initial condition, you can see the equation that satisfies this equation with the given initial condition.

We are going to use the equation:

Select the [mode] key. Choose option Graph and then 6: DIFF EQUATION
 

Press Enter twice.

Now go to the [Y=] editor and type in the equation and the initial condition.

Notice we are using y1 not y! Now press GRAPH.

There is the solution curve together with the field of slopes tangent to it

.

How to solve a Differential Equation Symbolically

Frome the Home window, go to [f3] tools and cursor down until you find the deSolve( command.

Type in the equation: y^' = e^t - 2 * y. To get the prime symbol use the [yellow] or [2nd] followed by the [=] on the TI-89, and on the TI-92 select [second] or [2nd] followed by the letter [b]. We are going to put the initial condition in as well and so we need to use the word and. You can simply type the word and in using surrounded by spaces using the keypad.  To get and from the menus, press [yellow] the [math] Select 8: Test
 
 

Then cursor down to the word and.

Your equation should look like:

deSolve( y^' = e ^t - 2 * y and y(0)=2,t,y)
 
 

The answer appears underneath it

Once you have solved a differential equation for the constant C, you may need to find a constant k, or perhaps solve for time. To do this, select the up arrow and highlight the solution you just found. Then press enter to auto paste it into the entry line.

Cursor to the beginning of the line and Press [f4] and select the Define command.

On the TI-89, you will need to cursor to the right of the variable y and change y = to y(t) = .  Press [enter]

Suppose we want to know when the value of y will be 5. We can use the solve( command. Press [f2] then select solve(.
 
 

Here is the result:

Part 2: You try it.

Find the slope fields and the equation that satisfies the initial condition. Also determine when the solution will have the value 0.75.

With y(0)= -1

With y(0)=1.