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In this paper, we consider the generalized Lane-Emden model which arises in the study of steller configuration. We came up with the nonlinear, multi-singular, initial value ordinary differential equations. Mathematical induction is used to verify the generalized non-iterative higher-order Lane-Emden type equation. We use various Homotopy Analysis Method (HAM) algorithms to find the convergent series solutions of the model. It is observed how the choice of initial value, increasing values of M in the polynomial nonlinearity yM, and different choices of HAM algorithms impact the solution radius of convergence. Convergent series solutions obtained from HAM algorithms are compared with the traditional power series and Runge-Kutta-Fehlberg method (RKF45). The traditional series solution follows the actual solution in the domain where the actual solution is positive while HAM does not require domain restriction.

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