Research Article A Reliable Treatment for Nonlinear Differential Equations H. R. Marasi, 1 M. Sedighi, 2 H. Aydi , 3,4,5 and Y. U. Gaba 5,6 1 Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran 2 Department of Mathematics, University of Bonab, Bonab 5551761167, Iran 3 Universit´ e de Sousse, Institut Sup´ erieur d’Informatique et des Techniques de Communication, Sousse 4000, Tunisia 4 China Medical University Hospital, China Medical University, Taichung 40402, Taiwan 5 Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa 6 Institut de Math´ ematiques et de Sciences Physiques (IMSP/UAC), Laboratoire de Topologie Fondamentale, Computationnelle et leurs Applications (Lab-ToFoCApp), Porto-Novo BP 613, Benin CorrespondenceshouldbeaddressedtoH.Aydi;hassen.aydi@isima.rnu.tnandY.U.Gaba;yaeulrich.gaba@gmail.com Received 25 December 2020; Revised 5 February 2021; Accepted 8 November 2021; Published 21 December 2021 AcademicEditor:RamJiwari Copyright©2021H.R.Marasietal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we use the concept of homotopy, Laplace transform, and He’s polynomials, to propose the auxiliary Laplace homotopyparametermethod(ALHPM).Weconstructahomotopyequationconsistingontwoauxiliaryparametersforsolving nonlineardifferentialequations,whichswitchnonlineartermswithHe’spolynomials.eexistenceoftwoauxiliaryparameters inthehomotopyequationallowsustoguaranteetheconvergenceoftheobtainedseries.Comparedwithnumericaltechniques, the method solves nonlinear problems without any discretization and is capable to reduce computational work. We use the methodfordifferenttypesofsingularEmden–Fowlerequations.esolutions,constructedintheformofaconvergentseries,are in excellent agreement with the existing solutions. 1. Introduction Initial value problems with singularity and of type Lane- –Emden differential equation, d 2 y dx 2 + 2 x dy dx + y r � 0, (1) have been used to model a large category of phenomena in various science, such as mathematical physics and astro- physics. e first studies on these equations have been published by Lane in 1870 [1]. A further research was continuedbyEmdenin[2].en,thisequationwasusedin the modeling of some problems, such as the thermal be- havior of spherical cloud of gas. In astrophysics and in the study of a self-gravitating sphericallysymmetricpolytropicfluid,thisequationappears as its gravitational Poisson’s equation. ere are several phenomena, such as astrophysics, aerodynamics, stellar structure, chemistry, biochemistry, and many others which canbemodeledbytheLane–Emdenequation[3–5].Fowler [6, 7] generalized the Lane–Emden equation to the Emden–Fowler equation: d 2 y dx 2 + 2 x dy dx + af(x)g(y)� 0, (2) forsomegivenfunctions f(x) and g(y).Inthisconnection, we note that the following heat equation, z 2 y zx 2 + r x zy zx + af(x, t)g(y)+ h(x, t)� zy zt , (3) where0 < x ≤ L, 0 < t < T,and r > 0,appearsinthemodeling of the diffusion of heat perpendicular to surfaces of parallel planes. For r � 2 and h(x, t)� 0 and for the steady state, equation (3) is the Emden–Fowler equation. Singularity behavior that occurs at x � 0 is a difficult element in the analysis of this type of equations, and due to this problem, common methods need to be reviewed. For example, Wazwaz [8] used the Adomian decomposition method to Hindawi Journal of Mathematics Volume 2021, Article ID 6659479, 5 pages https://doi.org/10.1155/2021/6659479