  Two-dimensional Eliashberg equations have been solved by use of a mixed
interaction with $s$- and $d$-channels.
  It is discussed what kind of pairing symmetry of the superconducting state
can be realized when the channel mixing parameters and the band-filling are
varied.
  By changing the mixing parameters and varying the chemical potential $\mu$
between zero- and half-filling, the pairing symmetry is determined and
summarized into a phase diagram of the symmetry. It is revealed that there is
an effective threshold in $\mu$ for the appearance of the d-wave
superconductivity regardless of the strength of the $d$-channel interaction. It
is also shown that, although the s-wave superconductivity can occur for any
value of $\mu$ if the $s$-channel interaction is mixed sufficiently, the d-wave
superconductivity has the advantage of achieving a high $T_{c}$ over the s-wave
one, once it occurs.
