Linear differential equations sometimes occur in which one or both of the functions p(t) and g(t) for y' + p(t) y = g(t) have jump discontinuities. If t0 is such a point of discontinuity, then it is necessary to solve the equation separately for tt0. Afterward, the two solutions are matched so that y is continuous at t0 ; this is accomplished by a proper choice of the arbitrary constants. The following problem illustrates this situation.
Note that it is impossible also to make y' continuous at t0.
Solve the initial value problem.
