Undergrad LIF Neuron Equation Solution for arbitrary time-dependent current (Neural Dynamics)

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The discussion focuses on the solution to the LIF neuron differential equation for arbitrary time-dependent current as presented in the book "Neural Dynamics." Participants are analyzing the steps taken by the author to derive this solution. The conversation emphasizes the mathematical techniques and concepts involved in solving the equation. Key points include the importance of understanding the underlying principles of neural dynamics. This exploration aids in comprehending how neurons respond to varying input currents over time.
gigorina
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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:
Screenshot 2024-01-07 at 21.49.10.png

Solution:
Screenshot 2024-01-07 at 21.49.02.png
 

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