In the presence of external sources, a superconducting weak link can be represented by a simplified model, consisting of a resistively shunted Josephson junction driven by a current source. We give in this paper, an analytical solution of the problem, in the case that the source current has both d. c. and a. c. components. As preliminary applications of our solution, we have also discussed square law detection and current steps of zero average voltage on the I-V characteristic, as the dimensionless a. c. component is small.