Define an antichronological ordering operator $\tilde{T}$


\begin{displaymath} \tilde T [A(t_1)B(t_2)]= \left\{ \begin{array}{ll} A(t_1) B(... ..._1 < t_2 )\\ B(t_2) A(t_1) & (t_1 > t_2 ) \end{array}\right . \end{displaymath} (1)

Define


\begin{displaymath} \tilde U (t,t_{o}) = \tilde T \exp \frac{1}{i} \int_{t_{o}}^{t} H(\tau)d\tau \end{displaymath}

What is the differential equation satisfied by $\tilde{U}$(t,0)?