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Unformatted text preview: Mathematics 421 Solution to ch. 4 rev 36 Spring 2008 Introduction Many students have difficulty solving differential equations with data defined by cases. Before attempting such a problem, it is useful to consider how to interpret the question in order to know what to expect of an answer. Since derivatives have the intermediate value property (even if they are not continuous), it is not strictly possible to solve a differential equation that would require a derivative to have a jump discontinuity. However, if the domain is broken at the locations of the jumps, a general solution of the equation can be found on each of remaining intervals. The initial value is used to find the solution on one of those intervals. There is a solution on an adjoining interval that takes any value at the point separating the intervals, so it is possible to find a solution that will be continuous across the location of the jump. This can be done for each jump to get a continuous function that satisfies the differential equation at all points where the derivative can exist....
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- Spring '08