Exploration of the Isoclines Applet
PROFESSOR: The isoclines applet. Let's explore graphs of solutions of differential equations using direction fields and isoclines. The first thing to do is to choose an equation from the pull-down menu here. And for this demonstration, I will choose the differential equation y prime equals y squared minus x. In the window at left, you can see the direction or slope field drawn. This is a representation of the differential equation. When I move the cursor over this window, a readout of the x- and y-coordinates shows up on the right-hand side of the screen. This is very useful in making measurements. If I click on the graphing window, the solution through the point that I've clicked on is drawn. This is an interesting function, probably one you've never seen before. Certainly, it's not an elementary function. Clicking some more points makes more solutions appear. In fact, every point on this plane has exactly one solution through it. This is the meaning of t...