Consider a 7th-order nonhomogeneous linear DE with constant coefficients a7y^7 + a6y^6 + a5y^5 + a4y^4 + a3y^3 + a2y^2 + a1y + a0y = fr. The characteristic equation of its associated homogeneous DE has the following roots: 1, -1, 0, 2i, 3i. And f(x) = xe^(-z).
a) Find the complementary function V for this DE.
b) Find the appropriate form of a particular trial solution yp of this DE. You don't have to solve for the undetermined coefficients in yp.