1. The problem statement, all variables and given/known data 1. y''' + y'' = 8x^2 2. y'' - 2y' - 3y = 4e^x - 9 2. Relevant equations Annihilator for any polinomial D^n+1 annihilator for e functions = e^ax = (D-a)^n 3. The attempt at a solution 1. getting the complementary eq. values of m = 0, 0, -1 yc= c1e^-x +c2 + xc3 then we multiply both sides by the annihilator D^3<D^2(D+1)> = 8x^2<D^3> we get y= c1e^-x +c2 + xc3 + x^2c4 + x^3c5 and from the original eq. the x^2 term has a coefficient of 8 therefore c4 = 8 sice there is no x^3 term then c5 should be zero ? and what about c4? the answer on the back says the answer is: c1+c2x+c3e^-x + 2/3 x^4 + 8/3x^3 + 8x^2 =========== 2.values of m=3, 2 yc=c1e^3x + c2e^-x if we multiply by the annihilator alpha = 1 in this case therefore annihilator would be (D-1) <D-1><D^2-2D-3>=4e^x-9 <D-1> so we have yc=c1e^3x + c2e^-x + c3e^x how do I go from there? thank you!