Notes on Diffy Qs - Sage demos for section 1.2

Press the Evaluate button below to launch the Sage demonstration. You may have to wait a little before the graph appears. Be patient. To change the function, you should edit the code and press the Evaluate button again. Note that Sage ignores any line starting with a pound sign #, so those lines are simply comments for a human.

Slope field

Here we plot the slope field of \(y' = f(x,y)\) where you can change the \(f(x,y)\) in the code, several possibilities are given. The default range is -2 to 2 in both x and y and you can change this as well by modifying the given variables.

If you do not need a fixed aspect ratio (x and y units are the same), remove the "aspect_ratio=1," from the above. If you want to plot more little lines, you can change the "plot_points=20" parameter.

Slope field and solution

In this demonstration we plot the slope field and have the compute draw a solution with a certain initial condition \(y(x_0)=y_0.\) The initial point is drawn as a red dot. Again you can change both the function and initial condition by editing the code and evaluating.