Use the annihilator method to show that if in (4) has the form , then equation (4) has a particular solution of the form , where is chosen to be the smallest nonnegative integer such that is not a solution to the corresponding homogeneous equation
is the form of particular solution.
A linear differential operator is said to annihilate a functionif for all x. That is, annihilates ifis a solution to the homogeneous linear differential equation (2) on.
Since is annihilated by so we have:
To check ifis solution of homogeneous equation then So take .
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