<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA^® 9.0.</p>

This research including, CO3O4 was prepared by the chemical spry pyrolysis, deposited film acceptable to assess film properties and applications as photodetector devise, studying the optical and optoelectronics properties of Cobalt Oxide and effect of different doping ratios with Br (2, 5, 8)%. the optical energy gap for direct transition were evaluated and it decreases as the percentage Br increase, Hall measurements showed that all the films are p-type, the current–voltage characteristic of Br:CO3O4 /Si Heterojunction show change forward current at dark varies with applied voltage, high spectral response, specific detectivity and quantum efficiency of CO3O4 /Si detector with 8% of Br ,was deliberate, extreme value with 673nm.