let g be an abelian group with identity e and hLet L(y) an y(n)(x) an 1 y(n 1)(x) a1 y(x) a0 y(x) where a0, a1, , an are fixed constants Consider the nth order linear differential equation L(y) 6e5x cos x 2xe5x () Suppose that it is known that Ly1(x) 3xe5x when y1(x) 12xe5x Ly2(x) 7e5x sin x when y2(x) 35e5x cos x Ly3(x) 7e5x cos x when y3(x) 35e5x cos x 70e5x sin x Find a particular solution to ()