Letwbe a generalized analytic function, that is.wsatisfies the equationHopf's maximum principle is used to derive sufficient conditions on the coefficientsAandBsuch that any solutionwof (*) satisfies the maximum principle of the formfor all = ∈Ğ, whereGis a bounded domain of the complex planeC. Furthermore a new factorization theorem is proved which asserts that any solutionwof (*) can be factorized in the formw=Wexp ω, whereWis a solution of an equation of the same type (*) with coefficientsÃ,[Btilde]andωis continuous inĞ. This factorization theorem allows to improve the constantCin the estimate |w(z)|≤Csupζ∈∂G|w(ζ)| obtained by means of the factorization by analytic functions.