In each part, find the solution of the initial value problem by the method of Laplace transforms.
y" − 6y' + 9y = e3x, y(0) = 0, y'(0) = 1.
Transforming both sides of the equation (as in the first part of this problem) gives
s2Y() − sy(0) − y'(0) − 6[sY () − y(0)] + 9Y () = 1/ − 3.
Plugging in the initial conditions gives
