Differential relationships between velocity and stress are derived from the kinetic theory of polymeric liquids. The Fokker-Planck equation corresponding to the so-called dumbbell theory for dilute solutions of polymers is considered. A Chapman-Enskog expansion for time-dependent, nonhomogeneous flows is proposed when the elastic character of the fluid is small, and the results included in the book of R. Bird, C. Curtiss, R. Armstrong, and O. Hassager [ Dynamics of Polymeric Liquids, Vol. 2, Kinetic Theory, John Wiley& Sons, New York, 1987] are recovered. A comparison with Oldroyd-B, FENE, and FENE-P fluids is presented in the frame of the plane Couette flow.