In recent years, research in Dew computing as a new layer in the vertical hierarchy of scalable computing has been developing. Directions for the development of this technology include research into the possibilities of Dew computing and its applications. Our research belongs to the second direction. We use this technology in a package of applied microservices for solving complex problems of the qualitative study of binary dynamic systems based on the Boolean constraint method in a hybrid cloud environment. This environment includes on-premises, high-performance, and cloud resources. In this paper, the usage of Dew computing technology in a hybrid cloud environment is discussed. A user dew agent installed on an on-premises resource is proposed to provide the possibility of the applied microservices package collaboration with cloud services in a hybrid cloud environment. The advantages of using a user dew agent are considered. The architecture, functionality, operation modes, and the installation of the dew agent are presented.