  We show how to reduce the nonlinear Wei-Norman equations, expressing the
solution of a linear system of non-autonomous equations on a Lie algebra, to a
hierarchy of matrix Riccati equations using the cominuscule induction. The
construction works for all reductive Lie algebras with no simple factors of
type G2, F4 or E8. A corresponding hierarchy of nonlinear, albeit no longer
Riccati equations, is given for these exceptional cases.
