  In this work, we investigate some connections between exact differential
equations and harmonic functions and in particular, we obtain necessary and
sufficient conditions for which exact equations admit harmonic solutions. As an
application, we consider the orthogonal trajectories of harmonic functions, and
among other results we obtain that the Cauchy-Riemann equations and the
non-vanishing of the first partial derivatives are sufficient for any two
curves to be orthogonal trajectories of each other. All curves throughout the
work are restricted to the xy-plane.
