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

• Published in: Applied mathematics and computation Vol. 218; no. 17; pp. 8359 - 8362
• Main Authors: Salinas-Hernández, E., Martínez-Castro, J., Muñoz, R.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.05.2012
• Subjects: Abel equation; Computation; Differential equations; Exact general solution; Functional transformations; Mathematical analysis; Mathematical models; Transformations; Abel equation; Exact general solution; Differential equations; Functional transformations
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2012.02.003

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.