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Singular initial value problems are investigated. We consider a new class of equations of Lane-Emden or Emden-Fowler type. The coefficient of y rewritten in terms of a new function ϕ(x) such that the equation can be solved in terms of ϕ. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method.

In this paper, singular initial value problems are investigated. We extend a decomposition method for different types of Emden-Fowler-like equations. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method. The solutions are constructed in the form of a convergent series.

In this paper, we consider a class of second‐order initial value problems. We extend the family of second‐order initial value problems for which the existence and uniqueness of a solution is known. To handle the singularity, we introduce the more general Caratheodory type of restrictions. The solvability results of the Emden–Fowler type of equations is established as a special case.Copyright © 2014 John Wiley & Sons, Ltd.

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