Differential Equations & CAS's: An Encounter with Uniquness

In this talk we discuss the danger of ignoring uniqueness criteria when solving an initial value problem either by a traditional pencil and paper approach or with computer algebra systems (CAS's). In particular, we consider both an exact ordinary first-order differential equation and one that may be solved using a basic solution technique such as separation of variables. In doing so, both analytic and numerical results are considered to emphasize the necessity of first analyzing the equation before attempting to solve it. We show that if we do not proceed with care our solutions to even these simple equations may be erroneous.