A coupling between Homotopy Continuation methods and Picard’s Method (HCPM) is proposed to provide an approximate solution to non-linear differential equations (NDE). By means of a simple case study, the solution calculated by HCPM will show lower relative error compared to Picard’s and HPM. Also, the solution calculated by HCPM has lower number of terms than Picard’s method and requires significantly fewer iterations than the employed by the HPM method.