  The Darboux transformation operator technique in differential and integral
forms is applied to the generalized Schrodinger equation with a
position-dependent effective mass and with linearly energy-dependent
potentials. Intertwining operators are obtained in an explicit form and used
for constructing generalized Darboux transformations of an arbitrary order. A
relation between supersymmetry and the generalized Darboux transformation is
considered. The method is applied to generation of isospectral potentials with
additional or removal bound states or construction of new partner potentials
without changing the spectrum, i.e. fully isospectral potentials. The method is
illustrated by some examples.
