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This paper deals with the Ulam stability of linear differential equations by using the method of variation of parameters, which provides a unified method to study the Ulam stability problem of linear differential equations of n-th order with constant and nonconstant coefficients. As an application of the main results, we also obtain the Hyers–Ulam stability of the Cauchy–Euler differential equations of second order, third order and n-th order. Our results make up to some deficiencies in the relevant literature. [ABSTRACT FROM AUTHOR]