Solved: In this problem you are led through the commands in Mathematica that enable you

Chapter 4, Problem 66

(choose chapter or problem)

In this problem you are led through the commands in Mathematica that enable you to obtain the symbolic Laplace transform of a differential equation and the solution of the initialvalue problem by finding the inverse transform. In Mathematica the Laplace transform of a function y(t) is obtained using LaplaceTransform [y[t], t, s]. In line two of the syntax, we replace Lap lace Transform [y[ t ], t, s] by the symbol Y. (If you do not have Mathematica, then adapt the given procedure by finding the corresponding syntax for the CAS you have on hand.) Consider the initial-value problem y" + 6y' + 9y = t sin t, y(O) = 2, y'(O) = -1. Precisely reproduce and then, in turn, execute each line in the given sequence of commands. Either copy the output by hand or print out the results. diffequat = y"[t] + 6y'[t] + 9y[t] == t Sin[t] transformdeq = LaplaceTransform [diffequat, t, s]/. {y[O] - > 2, y'[O] - > -1, LaplaceTransform [y[t], t, s] - > Y} soln = Solve[transformdeq, Y] II Flatten Y = YI. soln InverseLaplaceTransform[Y, s, t]