%0 Journal Article %T Explicit solutions of the $\mathfrak{a}_1$-type Lie-Scheffers system and a general Riccati equation %A Gabriel Pietrzkowski %J Mathematics %D 2014 %I arXiv %R 10.1007/s10883-012-9159-y %X 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. %U http://arxiv.org/abs/1403.4181v1