In our preceding article, by applying the results of Bieberbach, Fatou and Picard, we have studied the domain of holomorphy of the solution of the Cauchy problem for the differential operator with coefficients of entire functions. In this article, by employing the results of the modular function and its ordinary differential equation, we give a remark on the domain of holomorphy of the solution of the Cauchy problem for the differential operator of principal part with polynomial coefficients.