  We investigate the solution of the gap equation for mixed order parameter
symmetry states as a function of filling using a two-dimensional tight-binding
model incorporating second-neighbor hopping for tetragonal and orthorhombic
lattice. The principal (major) component of the order parameter is taken to be
of the $d_{x^2-y^2}$ type. As suggested in several investigations the minor
component of the order parameter is taken to be of the $d_{xy}$ type. Both the
permissible mixing angles 0 and $\pi /2$ between the two components are
considered. As a function of filling pronounced maxima of $d_{x^2-y^2}$ order
parameter is accompanied by minima of the $d_{xy}$ order parameter. At fixed
filling, the temperature dependence of the two components of the order
parameter is also studied in all cases. The variation of critical temperature
$T_c$ with filling is also studied and $T_c$ is found to increase with
second-neighbor hopping.
