A shooting method is used to determine a solution to a third-order ODE modeling the steady profile of a non-Newtonian thin droplet. We compare a direct approach to an iterative approach using a secant method. We obtain a nonlinear relationship between the contact angle and the position of the contact line . From this nonlinear relationship we use curve fitting to obtain an empirical law of the form where is the power law coefficient and is a nonlinear function of .