The general time-dependent LIF model solution is: $$ u(t) = u_{\text{rest}} \exp \left(-\frac{t-t_0}{\tau_m}\right) + \frac{R}{\tau_m}\int_0^{t-t_0} \exp\left(-\frac{s}{\tau_m}\right) \, I(t-s) \,\mathrm d s $$ From the LIF equation $$ \tau_m \frac{du}{dt} = R I(t) - [u(t) - u_{\text{rest}}] $$ According to this paper, equation 7.
It is assumed $t_0$ is the beginning of the time interval, at which $u(t)$ is at it's minimum and that $I(t)$ can vary. I have no idea where to even start, thank you.