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We consider a linear Hopfield network for solving quadratic programming problems with equation constraints. The problem is reduced to the solution of the ordinary linear differential equations with arbitrary square matrix. Because of some properties of this matrix the special methods are required for good convergence of the system. After some comparative study of neural network models for solving this problem we suggest a new model with the increased number of variables. This model is simple in implementation on the base of the linear Hopfield network and demonstrates sufficiently good convergence to the solution.