A family of nonlinear ordinary differential equations with arbitrary order is obtained in the non-extensive statistical mechanics scenario based on the Tsallis entropy. It is developed explicitly a WKB-like method for second order equations and it is applied to solve approximately a class of equations that contains as special case the Thomas -Fermi equation for a free neutral atom and heavy ion subjected to a strong magnetic field. It is expected that the procedure presented here can be useful in the discussion of other nonlinear processes.
Tsallis entropy; WKB method; nonlinear differential equations
