  Integrable systems of the sine-Gordon/Liouville type, which arise from
reducing the BPS equations for solutions invariant under 16 supersymmetries in
Type IIB supergravity and M-theory, are shown to be special cases of an
infinite family of integrable systems, parametrized by an arbitrary real
function $f$ of a real variable. It is shown that, for each function $f$, this
generalized integrable system may be mapped onto a system of linear equations,
which in turn may be integrated in terms of the two linearly independent
solutions of an ordinary linear second order differential equation which
depends only on the function $f$.
