In the present paper, we establish an existence theorem for non-homogeneous differential inclusions in Sobolev spaces. This theorem extends the results of Müller and Sychev [S. Müller and M. A. Sychev, Optimal existence theorems for nonhomogeneous differential inclusions, J. Funct. Anal. 181 2001, 2, 447-475; M. A. Sychev, Comparing various methods of resolving differential inclusions, J. Convex Anal. 18 2011, 4, 1025-1045] obtained in the setting of Lipschitz functions. We also show that solutions can be selected with the property of higher regularity.