  In view of the current interest in d_{x^{2}-y^{2}}+id_{xy} superconductors
some of their thermodynamic properties have been studied to obtain relevant
information for experimental verification. The temperature dependence of the
specific heat and superfluid density show marked differences in
d_{x^{2}-y^{2}}+id_{xy} state compared to the pure d-wave state. A second order
phase transition is observed on lowering the temperature into a
d_{x^{2}-y^{2}}+id_{xy} state from the d_{x^{2}-y^{2}} state with the opening
up of a gap all over the fermi surface. The thermodynamic quantities in
d_{x^{2}-y^{2}}+id_{xy} state are dominated by this gap as in an s-wave
superconductor as opposed to the algebraic temperature dependence in pure
d-wave states coming from the low energy excitations across the node(s).
