The general solution of the Ornstein-Zernike equation presented by Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] is further discussed. By applying the Hilbert transform, the first-order factorization and direct correlation functions (DCF) are generally and analytically obtained, with emphasis on the mean spherical approximation (MSA) for Yukawa fluids. These analytical results are employed to produce a new DCF for hard spheres through integrating with the previous generalized mean spherical approximation [J. Chem. Phys. 103, 7463 (1995)]. The new DCF is of simple analytical form and remedies the deficiencies of its Percus-Yevick version at high densities. Comparisons between the first-order and full MSA solutions are also made. It is shown that the two solutions give very close results for thermodynamic properties in the phase stable region and phase coexistence curves away from the critical point. At unstable states, the first-order MSA looks more advantageous when applications go beyond homogeneous. (C) 2003 American Institute of Physics.