Put a box around the result of a computation. If y = f (t) and y = g(t) are solutions of the di erential equation y + 4y + 2y = et , then |f (t) g(t)| goes to zero as t goes to + . Brie y justify your answer: (13 points) (a) (4 points) let (t) denote the solution to the initial value problem y = yt, y(0) = 0. Use the euler method with step size 1/2 to estimate (1). (b) (3 points) suppose you are using the euler method on an initial value problem y = f (t, y), y(0) = 1. Suppose that there is a solution curve through the point (0, 1) which is a straight line. The system is acted on by an external force of 8 sin(8t) pounds. If the mass is pulled down three inches and then released, determine the position of the mass at any time. (be careful.
