  In this work, we carry out a detailed study on the linearization of
isochronous centre of a modified Emden equation with linear external forcing.
We construct inverse integrating factor and time independent first integral for
this system through Darboux method. To linearize the isochronous centre we
explore a transverse commuting dynamical system and its first integral. With
the help of first integrals of the original dynamical system and its transverse
commuting system we derive the linearizing transformation and reduce the
nonlinear system into linear isochronous one. We also point out certain
mathematical structures associated with this dynamical system.
