Sagdeev's pseudo potential method is employed to study dust acoustic solitary waves in an unmagnetized plasma containing negatively charged dusts with non-thermal electron and ion. The range of parameters for the existence of solitary waves using the analytical expression of the Sagdeev potential has been found. It is observed that, depending on the values of the plasma parameters like ion to electron temperature ratio σ, non-thermal parameters β and γ, electron to ion density ratio μ, and the value of the Mach number M, both rarefactive and compressive solitary waves may exist.

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