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.Comment: 12 page
