  In this note we address the exact solutions of a time-dependent Hamiltonian
composed by an oscillator-like interaction with both a frequency and a mass
term that depend on time. The latter is achieved by constructing the
appropriate point transformation such that it deforms the Schr\"odinger
equation of a stationary oscillator into the one of the time-dependent model.
Thus, the solutions of the latter can be seen as deformations of the well known
solutions of the stationary oscillator, and thus an orthogonal set of solutions
can be determined in a straightforward way. The latter is possible since the
inner product structure is preserved by the point transformation. Also, any
invariant operator of the stationary oscillator is transformed into an
invariant of the time-dependent model. This property leads to a straightforward
way to determine constants of motion without requiring to use ansatz.
