In this project report, singular initial value problems, linear and non-linear, homogeneous and non-homogeneous of Lane-Emden-type equations are solved by using Taylor series, Residualpower series, and Adomain decomposition methods. To apply these methods; the Lane-Emdentype equation is solved analytically in the presence of singular point at x=0, to generate results for higher order derivatives and it shows a form of convergent series of the solution. The class of singular equation was generalized by changing the coefficient of , and the proposed technique was presented in a general way. The methods are illustrated with some examples, to yield exact results; several test problems have been presented to demonstrate the variability and practical usefulness of the methods. From these methods; ADM gives a better rapid convergent series with components that are elegantly computed to the solution. It is observed that the methods are easy to implement, valuable for handling singular phenomena, yields exact solution with easily computable terms.