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MURPHYS2016Agraïments: The first author is supported by FONDECYT Postdoctoral fellowship 3150131/2015 and was supported by the grant FPU AP2009-1189.Abstract. We prove that the differential equation x''x 1 = 0 has continuous weak periodic solutions and compute their periods. Then, we use the Harmonic Balance Method until order six to approximate these periods and to illustrate how the accuracy of the method increases with the order. Our computations rely on the Grobner basis approach

Weak periodic solutions of xẍ + 1 = 0 and the Harmonic Balance Method