In this problem you will solve the non-homogeneous differential equation y" +12y + 32y = sin(e) (1) Let C and C be arbitrary constants. The general solution to the related homogeneous differential equation y" +12y' + 32y = 0 is the function y(x) = C y(x) + C y(x) = C +C NOTE: The order in which you enter the answers is important; that is, Cf(x) + Cg(x) # C9(x) + Cf(x). (2) The particular solution y(a) to the differential equation y" +12y + 32y = sin(e) is of the form y(x) = y(x) u(x) + y(x) u(x) where u(x) = thus yp(x) = (4) The most general solution to the non-homogeneous differential equation y" +12y + 32y = sin(4x) y = C++ (3) It follows that u(x) = and u(x)= A and u(x)= is