Generating function for coloured graphs with tails satisfies a system of partial differential equations generalizing the Burgers equation. This system of differential equations admits an explicit recurrent solution in terms of genus expansion. The corresponding system of differential equations for the initial term of the genus expansion is equivalent to a functional equation concerning the inversion problem for certain formal power series. This solution immediately provides the Bass-Connell-Wright Tree Inversion Formula which was invented (in quite different terms) in 1982 in connection with the Jacobian Conjecture. At the same time consideration of these equations provides some other recent developments in the Jacobian Conjecture by W. Zhao and D. Wright.