  We explore the conditions for the existence of Noether symmetries in the
dynamics of FRW metric, non minimally coupled with a scalar field, in the most
general situation, and with nonzero spatial curvature. When such symmetries are
present we find general exact solution for the Einstein equations. We also show
that non Noether symmetries can be found.
  Finally,we present an extension of the procedure to the Kantowski- Sachs
metric which is particularly interesting in the case of degenerate Lagrangian.
