### 8.14.1. The Annihilator Method

The**
annihilator method** can be applied to find a particular solution for the
equation
L(
y
)=R
if

1.
*L* is a constant coefficient operator.

2.
*R* is annihilated by another constant
coefficient operator *A*, i.e.,
A(
R
)=0
.

The priniciple of the method is
simple. Applying *A* to
L(
y
)=R
gives
AL(
y
)=0
,
which must be satisfied for all *y*
that satisfy
L(
y
)=R
. Since *AL* is also a
constant coefficient operator, we can determine its null space
N(
AL
)
via its associated polynomial. The problem then reduces to selecting one
y
1
∈N(
AL
)
that also satisfies
L(
y
)=R
.