In this paper, the problem of pole placement by static output feedback is addressed. The systems under consideration are given by implicit linear time-invariant differential equations which are assumed to be completely controllable and observable. By means of an image representation of these systems, the pole placement problem can be easily formulated by a multilinear mapping. The application of an adapted Gauss-Newton method to the defining multilinear equations results in a very quickly converging algorithm. The performance of this algorithm is illustrated in detail on the well-known example of an inverted pendulum on a cart.