Concept explainers
Discontinuous Forcing Term. In certain physical models, the nonhomogeneous term, or forcing term,
may not be continuous but may have a jump discontinuity. If this occurs, we can still obtain a reasonable solution using the following procedure. Consider the initial value problem
where
a. Find a solution to the initial value problem for
b. Find a general solution for
c. Now choose the constants in the general solution from part (b) so that the solution from part (a) and the solution from part (b) agree, together with their first derivatives, at
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Chapter 4 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
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