TY - JOUR
T1 - New general solutions to the Abel equation of the second kind using functional transformations
AU - Salinas-Hernández, E.
AU - Martínez-Castro, J.
AU - Muñoz, R.
PY - 2012/5/1
Y1 - 2012/5/1
N2 - 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)=aξ1 2 and f(ξ)= eaξ. Finally, the case F(ξ)=ξ, where the necessity and difficulty of finding ξ becomes explicit, is analyzed.
AB - 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)=aξ1 2 and f(ξ)= eaξ. Finally, the case F(ξ)=ξ, where the necessity and difficulty of finding ξ becomes explicit, is analyzed.
KW - Abel equation
KW - Differential equations
KW - Exact general solution
KW - Functional transformations
UR - http://www.scopus.com/inward/record.url?scp=84859428106&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2012.02.003
DO - 10.1016/j.amc.2012.02.003
M3 - Artículo
SN - 0096-3003
VL - 218
SP - 8359
EP - 8362
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 17
ER -