Abstract
This paper shows that the following nonlinear boundary value problem where -1 and y is defined as a modified error function, can be reduced to the boundary value problems for the generalized Emden-Fowler equation and Abel differential equation of the second kind in the canonical form, which do not usually have closed-form solutions. The existence and uniqueness of the solution are established by considering another contraction mapping. Highly accurate approximate solutions of this problem are also provided.