Narrator: Problem 6-1: Finding a direction field for a differential equation.
We have a Task Template that we can use for this. It's in the section Differential Equations, which is split into ODEs and PDEs and then Direction Field.
Well, here's our differential equation. [Highlights with his mouse the equation: y2 = x2 - 2y - y2 under the Problem 6-1 heading.]
Let's...copy...this right-hand side [meaning the right-hand side of the equation, to the right of the =] and then if we use the tab key we'll move [he tabs until the right-hand side of the placeholder equation is selected] and select the right-hand side of the placeholder then we only have to paste in the differential equation that we copied. Hit the enter key. Let's keep the same viewing window 0 to 1 in each direction [he types in 0..1 into the cells next to the words ‘set an x-range of the form a..b’ and ‘set a y-range of the form c..d’] and then hit the enter key, which executes the DEplot command that draws the direction—the arrows of the direction field.
If we add initial points…and here are 4 initial points…and re-execute the command then solutions emanating from those initial points are added to the direction field.