Generalized Bernoulli Wick differential equation

Based on the distributions space on 𝒮ℂ′ (denoted by ℱ𝜃∗(𝒮′ ℂ)) which is the topological dual space of the space of entire functions with exponential growth of order 𝜃 and of minimal type, we introduce a new type of differential equations using the Wick derivation operator and the Wick product of elements in ℱ𝜃∗(𝒮′ ℂ). These equations are called generalized Bernoulli Wick differential equations which are the analogue of the classical Bernoulli differential equations. We solve these generalized Wick differential equations. The present method is exemplified by several examples.