New general solutions to the Abel equation of the second kind using functional transformations

Abstract A new method for solving the Abel equation of the second kind yy ′ = F 1 ( x ) y + F 0 ( x ) using functional transformations of the form y = f ( ξ ( z ( x ) ) ) is presented. It is important to say that the method depends on the possibility of finding ξ . The method is illustrated for the cases f ( ξ ) = a ξ 1 2 and f ( ξ ) = e a ξ . Finally, the case F ( ξ ) = ξ , where the necessity and difficulty of finding ξ becomes explicit, is analyzed.