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Based on the combined work of extended Krylov-Bogoliubov-Mitropolskii method and harmonic balance (HB) method an analytical technique is presented to determine approximate solutions of nonlinear differential systems whose coefficients change slowly and periodically with time. Furthermore, a non-autonomous case also investigated in which an external force acts in this system. Formulation as well as determination of the solution is systematic and easier than the existing procedures. The method isdoi:10.26782/jmcms.2018.10.00001 fatcat:s5zibgrbvvcydikrquzozyly7a