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We give explicit solutions for utility optimization problems in the presence of Knightian uncertainty in continuous time with nondominated priors and finite time horizon in a diffusion model. We assume that the uncertainty set is compact and time dependent on [0, T]. We solve the robust optimization problem explicitly both when the investor has logarithmic and exponential utility. To the best of our knowledge, this is the first work in deriving explicit solutions for utility maximization problems in a diffusion setting with time varying uncertainty sets both on drift and volatility.