Summary: This note is concerned with an iterative functional-differential equation \(x'(z)=c_1x(z)+\cdots+c_mx_{(m)}(z)\), where \(x_{(k)}(z)= x(x(\dots x(z)))\) is the \(k\)th iterate of the function \(x(z)\). The authors apply the techniques developed by J. Si, W. Li and S. S. Cheng [Comput. Math. Appl. 33, No. 6, 47-51 (1997; Zbl 0872.34042)] which deals with the simpler equation \(x'(z)=x_{(m)}(z)\) and they obtain analytic solutions to the more general equation.