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A particular solution for any inhomogeneous linear second, third,
and fourth order ordinary differential equation is generally
determined. Applying what was determined thus; and following by
example a particular solution formula for arbitrary order is
obtained. Finding a particular solutions to a linear inhomogeneous
ordinary differential equation has always been a process of
determining homogeneous solutions, and then adding any particular
solution of the inhomogeneous equation. The well-known methods of
undetermined coefficients and variation of parameters have long
been the standard in determining this particular solution. The
former has sometimes been considered 'ad-hoc', and both can be
intricate. A relatively simple formuila has been found which allows
the particular solution to be written and evaluated immediately.
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