Cheillini integrability and quadratically damped oscillators
  In this paper a new approach to study an equation of the Lienard type with a strong quadratic damping is proposed based on Jacobi's last multiplier and Cheillini's integrability condition. We obtain a closed form solution of the transcendental characteristic equation of the Lienard type equation using the Lambert W-function. 
Ankan Pandey, A. Ghose Choudhury, Partha Guha
nlin.SI