It was shown by Costa and Levine that the homogeneous differential equation (1-x[superscript N])y([superscript N]) + A[subscript N-1]x[superscript N-1)y([superscript N-1]) + A[subscript N-2]x[superscript N-2])y([superscript N-2]) + ... + A[subscript 1]xy[prime] + A[subscript 0]y = 0 has a finite polynomial solution if and only if [for all][subscript r], 0 [less than or equal to] r less than N, [there exist][subscript n] [greater than or equal to] 0 such that n mod N = r where n is a root of the recurrence relation. In this note, the case in which the equation has a forcing term on the right-hand side is considered. This forcing term is selected in such a manner that, given appropriate initial conditions, a particular solution will result that matches a finite portion of the infinite series homogenous solution, and at the same time, annihilates this infinite series homogeneous solution. The result of these initial conditions and this right-hand side is a solution that is a polynomial. The results obtained apply to the classical equations of Hermite, Legendre and Chebyshev with appropriate forcing terms and initial conditions.