Answer Happy

Consider the initial value problem y-2y = 3et, y(0) = a, where a is a constant. a). Find the solution of the initial value problem. b). How does the solution of the initial value problem behave as too? Does the behaviour depend on the initial value a? If yes, find the critical value of a for which transition from one type of behaviour to another happens. Denoting this critical value of a by ao use Matlab to plot solutions to three choices of a: a <ao, a = ao and a> ao. Use the same graph to plot all three solutions and choose a large enough interval for t to demonstrate the difference in the behaviour of solutions.