  Exact solutions are studied in the context of modified Brans-Dicke theory.
The non-linearity of the modified Brans-Dicke field equations is treated with
the Euler-Duarte-Moreira method of integrability of anharmonic oscillator
equation. While some solutions show a forever accelerating nature, in some
cases there is a signature flip in the evolution of deceleration parameter in
recent past. Importance of these latter models are studied in the context of
late-time acceleration of the universe. Constraints on the model parameters are
obtained from Markov Chain Monte Carlo (MCMC) analysis using the Supernova
distance modulus data, observational measurements of Hubble parameter, Baryon
acoustic oscillation data, and the CMB Shift parameter data.
