I don't agree with the DE. Try to set up the homogeneous case (the one without the impressed force) first:
. You've got two forces present: the spring force and the damping force. Spring forces look like the following (at least in the regime of Hooke's Law): . You're told that a force of 2 pounds stretches the spring 6 inches. That tells you that , as I think you've already computed. is always positive in these cases. The mass is 2 pounds. The damping force acts in a direction opposite to the spring force, correct? It's going to have to have the opposite sign.
So let's say that . How does that look to you? Can you finish writing the DE, including the impressed force?