Abstract: Two conclusions have been achieved in this paper.Firstly, a formal solution of the equations ∇×E=ω, ∇·E=P has been derived with different point of view from commonly known classical method developed by He-lmholtz(1),(2),(3).Secondly, a method to construct a vector field with given curl function and divergence function has been given in terms of the above solution.

Key words: Hilbert space, system of differential equations, two-point boundary value problem, solution