In this paper we focus on estimating the parameters in the stochastic differential equations (SDE's) with drift coefficients depending linearly on a random variables ∅ and .The distributions of the random effects ∅ and are depends on unknown parameters from the continuous observations of the independent processes ( ( ), ∈ [0, ], = 1, … , ). When is an unknown parameter or restrict positive constant also studied in this paper. We propose the Gaussian distribution for the random effect ∅ and the exponential distribution for the random effect , we obtained an explicit formulas for the likelihood functions in each case and find the maximum likelihood estimators of the unknown parameters in the random effects and for the unknown parameter . Consistency and asymptotic normality are studied just when ∅ is normal random effect and is constant.