  An integro-differential equation satisfied by an eigenvalue density defined
as the logarithmic derivative of the average inverse characteristic polynomial
of a Wilson loop in two dimensional pure Yang Mills theory with gauge group
SU(N) is derived from two associated complex Burgers' equations, with viscosity
given by 1/(2N). The Wilson loop does not intersect itself and Euclidean
space-time is assumed flat and infinite. This result provides an extension of
the infinite N solution of Durhuus and Olesen to finite N, but this extension
is not unique.
