ODEs Annihilator question.

So, Im given the equation $$y''-y=t^2e^t$$, and told to use the method of annihilators. After googling annihilators it seems to me the first step is to solve the characteristic equations of L(y) = 0 .

So, this means finding the annihilator for the right-hand side. I believe it is (D-1)^3 but can anyone confirm this before I go further on a bad assumption?

Question

ODEs Annihilator question. 

So, Im given the equation $$y''-y=t^2e^t$$, and told to use the method of annihilators. After googling annihilators it seems to me the first step is to solve the characteristic equations of L(y) = 0 .

So, this means finding the annihilator for the right-hand side. I believe it is (D-1)^3 but can anyone confirm this before I go further on a bad assumption?

anonymous · Answer

Anybody? Confirm/deny the annihilator for t^2e^t is (D-1)^3?

anonymous · Answer

Ok fine. Assuming it is. My next step is to apply it to both sides, and then solve L_1 * L(y) . 

which i think is: $$(D-1)^3 (D+1)(D-1) = 0 $$

which has the roots 1, -1.