How can I graph an implicit equation on my TI-89/92 calculator?

[NeutronStar]

I have a TI graphing calculator and I'd like to graph the following equation,...

$$x^3+y^3-3xy = 0$$

I'm not sure how to graph this on my TI

I took the derivative of the above with respect to x,...

$$3x^2+3y^2\frac {dy}{dx}-3x\frac{dy}{dx}-3y=0$$

Which I solved as,...

$$\frac{dy}{dx}=\frac{y-x^2}{y^2-x}$$

I'd also like to graph this differential field if possble.

Any suggestions for graphing either the original equation or the differential equation?

I have access to both the TI-89 and the TI-92 calculators. Thanks.

 

[Townsend]

The TI 89, 92, voyage 200 or the 89 platinum edition are all very similar. For any of these calculators to graph a function you must solve the equation explicitly for the dependent variable in terms of the independent variable. If you want to be able to graph an equation that is not a function you will need some computer software. I would recommend winplot because it is free and very easy to use.

To graph a slope field you must set your calculator graphing mode to Differential Equations mode. On my voyage 200 I have a mode button that will allow me to access the options page so I can set my graphing mode to Differential equations. Once you are in the diff eq mode then proceed to your y= window where you can then enter your diff eq as dy/dx. The next line below that is for your initial conditions. That should get you started but you really should refer to the manual for the calc. The PDF version is free online from texas instrument. I believe the web addy is http://education.ti.com/us/product/tech/89/guide/89guideus.html

Best of luck

 

[franznietzsche]

I have an 89 and have had it for a few years, so I'mvery familiar with it. It can only graph explicit functions and slope fields for linear first order ODEs.

So you can't graph any of those.

 

[Justin Lazear]

The 89 can graph implicit functions of 2 variables and slope fields. It can probably even do the latter for equations of higher order than one.

Set your graphing mode to 3D. Go to the y= menu and enter the implict equation into one of the slots. Then go to the Format menu (either from the F1 menu or press Diamond / | , the one right above EE) and for style, select Implicit Plot.

It can also do the slope field plot. Set the mode to DEQs, enter your equation (don't forget the indeces on the y's), and then in the Format menu set Fields to SLPFLD.

--J

 

[NeutronStar]

The 89 can graph implicit functions of 2 variables and slope fields. It can probably even do the latter for equations of higher order than one.

Set your graphing mode to 3D. Go to the y= menu and enter the implict equation into one of the slots. Then go to the Format menu (either from the F1 menu or press Diamond / | , the one right above EE) and for style, select Implicit Plot.

It can also do the slope field plot. Set the mode to DEQs, enter your equation (don't forget the indeces on the y's), and then in the Format menu set Fields to SLPFLD.

--J

Thanks Justin!

I knew the calculator could do it, I just wasn't familiar enough with how to run it. I didn't realize that the 3-D mode could also do implicit functions. I also didn't realize that the differential equations feature would accept the y1 without having to define it explicitly. That's cool!

This was almost too easy. It's like magic.

 

[NeutronStar]

Winplot

If you want to be able to graph an equation that is not a function you will need some computer software. I would recommend winplot because it is free and very easy to use.

I was able to graph them on my TI implicitly as Justin described. But I also downloaded that Winplot program and was able to graph everything on there as well.

Thanks for the tip about Winplot. That's a nifty little program.

I was able to plot both the implicit equation and the derivative field in the same window in Winplot. I've enclosed the results of that plot in the attachment in case anyone is interested in seeing the capabilities of Winplot.