The solution of the Euler-Lagrange equations for the director components ny=f1(z)sinqy and nz=f2(z)cosqy, where q is the wave number of the flexoelectric domains of Vistin'-Pikin-Bobylev, has been for the first time exactly found with the aid of matrix calculations for the case of a planar nematic layer with anisotropic elasticity and a negative dielectric anisotropy under the simultaneous action of an inhomogeneous DC flexoelectrically deforming electric field and a.c. dielectrically orienting electric field. Experimental illustration is given for the influence of the additionally applied AC voltage on the behaviour of the flexoelectric domains.