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Let {Pn(x)} ∞ n=0 be a sequence of polynomials of degree n. We deÿne two sequences of di erential operators n and n satisfying the following properties: n(Pn(x)) = Pn−1(x); n(Pn(x)) = Pn+1(x):By constructing these two operators for Appell polynomials, we determine their di erential equations via the factorization method introduced by Infeld and Hull (Rev. Mod. Phys. 23 (1951) 21). The di erential equations for both Bernoulli and Euler polynomials are given as special cases of the Appell polynomials.

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