Learning Guide Learning Guide

260 • Chapter 6: Examples from CalculusPiecewise Functions The piecewise command allows you to constructcomplicated forcing functions by approximating sections of it with analyticfunctions, and then taking the approximations together to representthe whole function. First, look at the behavior of piecewise.> f:= x -> piecewise(1 plot(f, 0..3);10.80.60.40.200.5 1 1.5 2 2.5 3Thus, you can use this piecewise function as a forcing function.> eq := diff(y(t),t) = 1-y(t)*f(t);eq := d ({ )1, if 1 − t ≤ 0 and t − 2 < 0;dt y(t) = 1 − y(t) 0, otherwise.> ini := y(0)=3;ini := y(0) = 3> sol3 := dsolve({eq, ini}, {y(t)}, type=numeric);