text: solve the given differential equation by annihilator method:-y'' + 4y' + 4y = 2x + 6?   i do not know if this is the 'annihilator method' but here goes:  y'' + 4y' + 4y = 2x + 6  first solve y'' + 4y' + 4y = 0 k^2 + 4k + 4 = 0  so (k + 2)^2 = 0 ie k = -2, -2 solution is y = ae^(-2t) + bte^(-2t)  now for particular solution  yp = ax + b yp' = a yp'' = 0 y'' + 4y' + 4y = ax + (4a + b) = 2x + 6 so a = 2 and 4a + b = 6  so b = -2  thus the general solution is y = ae^(-2t) + bte^(-2t) + 2x - 2