This is essentially the Technical Writing Exercise number 2 on page 251, with more elaborate instructions.
Consider the differential equation
where b is a constant. Describe how the behavior of solutions to this equation changes as b varies.
To help organize your answer, think of b as a point on a line, and divide that line into regions where the solutions are of the same type.
There will be exceptional points where the solution changes type. Discuss the behavior of the solutions as b approaches these points. In particular, can you see how the behavior at each exceptional point arises as the transition from one type to the other.
Also, be sure to consider the effect of the sign of b and discuss what happens as b goes to plus or minus infinity.
You may find it useful to plot solutions for various values of b using MATLAB or Richard Mansfield's JAVA applet.
You should sketch, or otherwise produce, representative graphs for carefully chosen values of b . Depending upon their size, your essay will probably be between 1 and 5 pages in length.
Due Monday, November 12, 2001, in class.