In the book Neural Dynamics: https://neuronaldynamics.epfl.ch/online/Ch1.S3.html
There is a solution to the following differential equation (LIF Neuron) for arbitrary time-dependent current. I was trying to figure out the steps the author took to get to the solution.
Original Equation:
$\tau_{m}\frac{du}{dt} = - [u(t) - u_{rest}] + RI(t)$
Suggested Solution:
$u(t) = u_{rest} + \frac{R}{\tau_{m}} \int_0^{\infty} e^{(-\frac{s}{\tau_m})}I(t-s)ds $