# Math Help - Annilator Method Error

1. ## Annilator Method Error

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.

2. Originally Posted by diddledabble
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 $e^{3x}$ is $\left(D-3\right)$ and the annihilator for $-x$ is $D^{\color{red}2}$.

Now, the annihilator of $e^{3x}-x$ is the product of the two individual annihilators: $D^2\left(D-3\right)$

Note that $D^3\left(D-3\right)$ also works as an annihilator, but $D^3$ really isn't necessary.

Now if the question was find the annihilator for $e^{3x}-x^2$, then the answer your book gives would be correct.

Does this make sense?