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In this paper, we study solutions of the quasilinear differential equation z_z f(z)+z_zf(z)+(1-|z|^2)_z_z f(z)=f(z). We utilize harmonic mappings to obtain an explicit representation of solutions of this equation. By this result, we give two versions of Landau-type theorem under proper normalization conditions. , number=3, journal=Journal of Mathematical Study, year=2014, month=Sept., pages=295–304