# Thread: Find the differential operator that annihilates

1. ## Find the differential operator that annihilates

$x^{2}e^{x}-xsin4x+x^{3}$

2. Originally Posted by diddledabble
$x^{2}e^{x}-xsin4x+x^{3}$
See this and see if you can figure it out from there.

Another thing to note is the following: If $L_1,L_2,L_3$ are annihilators of $f(x),g(x),h(x)$ respectively, then $L_1L_2L_3$ annihilates $f(x)+g(x)+h(x)$.

3. Originally Posted by diddledabble
$x^{2}e^{x}-xsin4x+x^{3}$
If you want to check.
Spoiler:

$(D-1)^3$ will annihilate the first, $\left(D^2+16\right)^2$ will annihilate the second while $D^4$ will do the third. Then compose the three operators.