  The Darbroux transformation is generalized for time-dependent Hamiltonian
systems which include a term linear in momentum and a time-dependent mass. The
formalism for the $N$-fold application of the transformation is also
established, and these formalisms are applied for a general quadratic system (a
generalized harmonic oscillator) and a quadratic system with an inverse-square
interaction up to N=2. Among the new features found, it is shown, for the
general quadratic system, that the shape of potential difference between the
original system and the transformed system could oscillate according to a
classical solution, which is related to the existence of coherent states in the
system.
