An important contribution to the integrability of non-linear differential equation, made by the E.S.Cheb.Terrab, is the Abel Inverse Riccati(AIR) equation. Recently I got an idea of making generalization of the equation using some technique introduced in Kamke's books. I wrote it in latex. I hope you guys can give me some advice. I have deleted some questions I asked before because I think it is more appropriate to create a post to share my ideas with you.final_version.pdf