If the constant-coefficient, linear differential equation
y^(5) + y^(p1) - 2y^(p2) + ky^(p3) - 8y^(p4) = 0
has the general solution
y = (A + Bx)e^(-x) + Ce^(2x) + D cos 2x + E sin 2x,
find the values of k, p3 and p4.
(a) k = -12, p3 = 1, p4 = 0
(b) k = -12, p3 = 2, p4 = 0
(c) k = 12, p3 = 2, p4 = 1
(d) k = -12, p3 = 1, p4 = 1
(e) k = 12, p3 = 1, p4 = 0