A set of partial differential equations are obtained that are equivalent to the gauge constraint functional equation in the temporal gauge for a set of vector bosons interacting through a Yang-Mills type Lagrangian. This is done by expanding the wave function in a functional power series. The first two orders are solved explicitly for the case of two space and one time dimension. A set of solutions is also presented of the gauge constraint equation to the first two orders for three space and one time dimension. A generalization to 3+1 dimensions of a conjecture in 2+1 dimensions made by Feynman for the ground state of this problem is examined. It is shown that the conjectured wave function satisfies the gauge constraint and Schrodinger equations to second order in the fields.