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

摘要

A new method for solving the Abel equation of the second kind yy′=F1(x)y+F0(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)=aξ12 and f(ξ)=eaξ. Finally, the case F(ξ)=ξ, where the necessity and difficulty of finding ξ becomes explicit, is analyzed.