Abstract
In this paper, we propose a direct method to obtain an implicit solution of the Abel equation of the second kind
[g(0)(x) + g(1)(x)u]u' = f(0)(x) + f(1)(x)u + f(2)(x)u(2).
We first reduce it into an equivalent equation, and assume that the coefficient functions f(i)(x), i = 0, 1, 2 and g(i)(x), i = 0, 1 satisfy the well-known Julia's condition. Therefore the given Abel equation can be transformed into a first order linear differential equation, which can be easily solved, and then the implicit solutions of this equation are obtained.