This note concerns the applications of the modulating function method to the input-output relation y(t)=

. The problem is to determine the coefficients c
kin the differential equation

from integral transforms of

and

over a finite interval [

]. The main objective is to present a device which obtains the c
k\´s via the inversion of a system of

linear equations, whereas the straightforward approach leads to a system involving twice as many equations.