We prove that if T is a theory of large, bounded, fields of characteristic zero, with almost quantifier elimination, and T_D is the model companion of T + D is a derivation, then for any model U of T_D, and differential subfield K of U whose field of constants is a model of T, and linear differential equation DY = AY over K, there is a Picard-Vessiot extension L of K for the equation which is embedded in U over K Likewise for logarithmic differential equations over K on connected algebraic groups over the constants of K and the corresponding strongly normal extensions of K.
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