Solutions of time-dependent Emden-Fowler type equations by homotopy-perturbation method

In this Letter, we apply the homotopy-perturbation method (HPM) to obtain approximate analytical solutions of the time-dependent Emden-Fowler type equations. We also present a reliable new algorithm based on HPM to overcome the difficulty of the singular point at x=0. The analysis is accompanied by some linear and nonlinear time-dependent singular initial value problems. The results prove that HPM is very effective and simple.