Discontinuous Coefficients. Linear differential equations
Chapter 2, Problem 33(choose chapter or problem)
Discontinuous Coefficients. Linear differential equations sometimes occur in which one orboth of the functions p and g have jump discontinuities. If t0 is such a point of discontinuity,then it is necessary to solve the equation separately for t < t0 and t > t0. Afterward, the twosolutions are matched so that y is continuous at t0; this is accomplished by a proper choice ofthe arbitrary constants. The following two problems illustrate this situation. Note in each casethat it is impossible also to make ycontinuous at t0. Solve the initial value problemy+ p(t)y = 0, y(0) = 1,wherep(t) =2, 0 t 1,1, t > 1.
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