  For a general differential system $\dot x(t) = \sum_{d=1}^3 u_d(t)X_d$, where
$X_d$ generates the simple Lie algebra of type $\mathfrak{a}_1$, we compute the
explicit solution in terms of iterated integrals of products of $u_d$'s. As a
byproduct we obtain the solution of a general Riccati equation by infinite
quadratures.
