In this paper, we investigate the conditions of being an harmonic curve and research differential equations characterizing any differentiable curve in Euclidean 3-space. By means of the Laplacian image of the mean curvature vector field of a curve, it is stated which type of harmonic the curve is. Then we write the theorems related to the characterization of the curves and proved these theorems. When the differentiable curve, used throughout this paper, is specifically  replaced to the unit speed curve then it is seen that the results coincide with the study [4].   In addition we elucidate the characterizations of helix as an example.