  Tracy-Widom (TW) equations for one-matrix unitary ensembles (UE) (equivalent
to a particular case of Schlesinger equations for isomonodromic deformations)
are rewritten in a general form which allows one to derive all the lowest order
equations (PDE) for spectral gap probabilities of UE without intermediate
higher-order PDE. This is demonstrated on the example of Gaussian ensemble
(GUE) for which all the third order PDE for gap probabilities are obtained
explicitly. Moreover, there is a {\it second order} PDE for GUE probabilities
in the case of more than one spectral endpoint.
  This approach allows to derive all PDE at once where possible, while in the
method based on Hirota bilinear identities and Virasoro constraints starting
with different bilinear identities leads to different subsets of the full set
of equations.
