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We present a method to solve initial and boundary value problems using arti ial neural networks. A trial solution of the di erential equation is written as a sum of two parts. The rst part satis es the initial/boundary onditions and ontains no adjustable parameters. The se ond part is onstru ted so as not to a e t the initial/boundary onditions. This part involves a feedforward neural network, ontaining adjustable parameters (the weights). Hen e by onstru tion the initial/boundary onditions are satis ed and the network is trained to satisfy the di erential equation. The appli ability of this approa h ranges from single ODE's, to systems of oupled ODE's and also to PDE's. In this arti le we illustrate the method by solving a variety model problems and present omparisons with nite elements for several ases of partial di erential equations.