Find the annihilator given y''-6y'+10y = e^(3x)-x
My book list the annihilator as D^3(D-3) but I don't understand how they got that. I am wondering if it might be a typo in the text.
The Annihilator for is and the annihilator for is .
Now, the annihilator of is the product of the two individual annihilators:
Note that also works as an annihilator, but really isn't necessary.
Now if the question was find the annihilator for , then the answer your book gives would be correct.
Does this make sense?