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**Summary:**Looking for guidance on how to model an RLC circuit with a system of ODES, where the variables are the resistor and inductor voltages.

This is a maths problem I have to complete for homework.

The problem is trying to prove that the attached circuit diagram can be modeled using the system of ODEs:

It says to do this using circuit laws, but I am having trouble working out what circuit laws to use that can allow me to create they system provided.

Any help would be appreciated.

Thanks.