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

Exact Differential Equations and Harmonic Functions