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Don't cheat! If you didn't do the exercise inÌýMathematicaÌýbefore you came here to see the discussion,Ìýgo backÌýand do it now!

Assuming that you did the exercise correctly, you should have produced a picture that was simply a larger version of the following:

Yet another one with horizontal isoclines.

The slope field has such a complicated flow to it that it's almost impossible to spot any kind of trend. This calls for further investigation!

Up until now, I've been telling you the setting I would recommend for theÌýVectorPointsÌýoption of theÌýVectorPlotÌýcommand. As you can see from the above results, sometimes it will be necessary for you to make a decision for yourself as to whether this option requires adjustment in order to get a better feel for the true nature of a slope field.

Just as a reminder, the original problem was to make the slope field of:

What I'd like you to do is go toÌýMathematicaÌý(in just a second—hold on) and make the following changes to the way you did the problem before:

• ChangeÌýthe plot bounds to: -5 ≤ÌýxÌý≤ 5, and -2Ï€ ≤ÌýyÌý≤ 2Ï€. This will provide us a larger overview of the plot field.
• IncreaseÌýtheÌýVectorPointsÌývalue to a higher value, (experiment a little if necessary)

Now go back toÌýMathematicaÌýand make these changes, coming back here when you are done.

Welcome back! Did you get a slightly better feel for the slope field now that you redid the exercise with the suggested changes? Obviously we now need toÌýfurther discussÌýour latest discoveries.