Some notes on using the homotopy perturbation method for solving time-dependent differential equations

Although attempts have been made to solve time-dependent differential equations using homotopy perturbation method (HPM), none of the researchers have provided a universal homotopy equation. In this paper, going one step forward, we intend to make some guidelines for beginners who want to use the homotopy perturbation technique for solving their equations. These guidelines are based on the LL part of the homotopy equation and the initial guess. Afterwards, for solving time-dependent differential equations, we suggest a universal LL and v0v0 in the homotopy equation. Examples assuring the efficiency and convenience of the suggested homotopy equation are comparatively presented.