Given a ($4\times4$ in the important case) matrix differential equation:
$\frac{d U_t}{dt}= A_t U_t$
where $U_t \in SU(n)$ and $A_t \in \mathfrak{su}(n)$.
What is the relationship between the solution $U_t$ to this equation and the solution to:
$\frac{d U_t}{dt}=f(t)A_tU_t$ where $f$ is some not too badly behaved real function? Can the new solution be easily expressed in terms of the old one?