An asymptotic solution has been obtained for the case of low collision frequency using a Fokker-Planck collision operator suitable for the study of the effect of electron-ion collisions on the 'Universal' instability in an inhomogeneous plasma. The solution, obtained under certain approximations, contains fractional powers of the collision-rate coefficient and this eliminates the divergence occurring in the expression for physical quantities like perturbed density when obtained by using a direct iterative method. Also, an approximate study of the solutions over various ranges of the velocity variable is given.