Auto generated differential equation for a series RLC circuit

[PA3041]

Dear Experts,

I need to verify whether, when designing a series RLC circuit, it is necessary to generate the differential equation based on the circuit design. Is there any software that can automatically generate the differential equation for a series RLC circuit? Does PROTEUS support it

I need to understand how the behavior of the differential equation changes when the components in a series RLC circuit are altered, especially when an additional voltage source is added. How does this transformation affect the equation from a homogeneous to a non-homogeneous form?

Thank you

 

[wwfeldman]

series RLC is likely in most intro texts
there are also a plethora of articles on them on the internet
maybe you want to look there