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Fluid stochastic (or hybrid) Petri nets with flush-out arcs are Petri net-based models with two classes of places: discrete places that carry a natural number of distinct objects (tokens), and fluid places that hold a positive amount of fluid, represented by a real number. For this kind of formalisms, equations can be automatically derived from the model. Such equations, however, are often too complex to be solved analytically and simple discretization techniques usually can be successfully applied only to simple cases. In this paper, we present a particular solution technique for transient solution that makes use of the Kronecker-algebra.