Sam and Sally are discussing how to solve y ′′
(t)+y(t)=u π/3
​
(t),y(0)=1,y ′
(0)=0. Sally says, "I don't need to know anything about Laplace transforms to do this. I can just use the methods I learned for higher order-equations and the Annihilator method. I'll first solve y ′′
+y=0,y(0)=1,y ′
(0)=0, that's easy, then I'll solve y ′′
+y=1 using the Annihilator method, making sure to pick the solution that has the same value for y( 3
π
​
) and y ′
( 3
π
​
) as my first solution did. By piecing the two solutions together, I'll have the solution to my problem. Sam replies, "That sounds like a lot more work than just using Laplace transforms." a.) Carry out the plan Sally has in mind, write your answer as a piece-wise defined function. b.) Do you agree with am? Why or why not? To answer this you should solve the problem using Laplace transforms and compare the amount of work to that in (a).