Explain why or why not Determine whether the

Chapter , Problem 47

(choose chapter or problem)

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. The general solution of a second-order linear differential equation could be y = ce2t - t2, where c is an arbitrary constant. b. If yh is a solution of a homogeneous differential equation y_ + py_ + qy = 0 and yp is a particular solution of the equation y_ + py_ + qy = f , then yp + cyh is also a particular solution, for any constant c. c. The functions 51 - cos2 x, 5 sin2 x6 are linearly independent on the interval 30, 2p4. d. If y1 and y2 are solutions of the equation y_ + yy_ = 0, then y1 + y2 is also a solution of the equation. e. The initial value problem y_ + 2y = 0, y102 = 4 has a unique solution.