Linear differential equations in exponential extensions

We present an algorithm for computing rational solutions of linear differential equations with coefficients in exponential extensions of monomial extensions of a base field. We focus on the system of generators describing the extension and show why some of the generators sets are more “suitable” than others. These results partially improve and generalize the method presented by Singer (J. Symbolic Comput. 11 (1991) 251) for finding Liouvillian solutions of linear differential equations with coefficients in Liouvillian extensions of C(x).