This lab is very versatile. Its successful use at KSU for over a decade impressively testifies to its quality.
One of the uses the author has in his book is an exercise in which students are to find an initial condition at x=-3 such that the solution is within a specific small range at x=4. This exercise forces students to use facts such as that solution curves will lay smoothly on the vectors of the direction field or such as that solution curves do not cross each other (under mild continuity conditions). In this fashion under the right guidance and with the right questions a ?trial and error? exercise makes students actively engage and use rather theoretical facts. An extension could be for students to devise a fastest possible automatic method to achieve the desired value at x=4. Invariably this would lead to bisection, thus showing that students should be ready to make connections between different parts of the curriculum.
Another possible use is the demonstration of stability of solutions. For an equation such as,
say y?=y(1-y) students could try to predict the shape of solution curves and one could ask them to try to find a curve that starts with y(-3)>0 and which does not converge to 1. The impossibility to find such a solution can lead to a discussion of how to predict from the DE that this will happen.