Inflationary solutions and inhomogeneous Kaluza-Klein cosmology in 4+n dimensions

We analyze the existence of inflationary solutions in an inhomogeneous Kaluza-Klein cosmological model in 4+n dimensions. It is shown that the 5-dimensional case is the exception rather than the rule, in the sense that the system is integrable (under the assumption of the equation of state $\rho= kp$) for any value of k. It is also shown that the cases k=0 and k=1/3 are integrable if and only if n=1.