The annihilator method solves certain nonhomogeneous linear ordinary differential equations with constant coefficients. Write the equation as
 |
where 
and 
is a differential operator. If another differential operator 
annihilates the forcing term, so that 
, applying 
to both sides gives a homogeneous
ordinary differential equation,
 |
Solutions of this enlarged equation include the complementary solution of the original equation and a trial form for its particular solution. Substitution in the original equation determines the remaining coefficients.
For example, the equation 
has 
, while 
annihilates 
. The enlarged homogeneous
ordinary differential equation supplies the trial term 
, and substitution gives 
.
