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 .