  Highly oscillatory differential equations present significant challenges in
numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz,
is a commonly employed tool as a numerical approximation method. In this
article, the Modulated Fourier Expansion is analytically derived for a linear
partial differential equation with a multifrequency highly oscillatory
potential. The solution of the equation is expressed as a convergent Neumann
series within the appropriate Sobolev space. The proposed approach enables,
firstly, to derive a general formula for the error associated with the
approximation of the solution by MFE, and secondly, to determine the
coefficients for this expansion -- without the need to solve numerically the
system of differential equations to find the coefficients of MFE. Numerical
experiments illustrate the theoretical investigations.
