Can an ODE accurately model an RLC circuit with additional sources?

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An ordinary differential equation (ODE) can model RLC circuits, but adding current sources complicates the equation significantly. Each source introduces conditions that may conflict with one another, affecting circuit behavior. Enforcing a voltage drop across a circuit with an ideal current source in series presents challenges, as the current source dominates. Similarly, in a parallel configuration, an ideal voltage source may render the current source ineffective. These complexities highlight the limitations of ODEs in accurately modeling circuits with multiple sources.
Jhenrique
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The equation for this physical model is:
http://upload.wikimedia.org/wikipedia/commons/f/fb/RLC_series_circuit_v1.svg

8a89f7d3622fc859d3bc910a8691b9e9.png


And for this is:
http://upload.wikimedia.org/wikipedia/commons/d/d0/RLC_parallel_circuit_v1.svg

8383fa6312eb5e0b7befb1b4172ae749.png



But and if now I add a source of current in those schemes, the ODE changes?

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These circuits do not really work. Each of the sources are going to require conditions that are at odds to the other.

Plus, how do you enforce a voltage drop across a circuit with an ideal current source in series? How do you enforce a current source in parallel to an ideal voltage source?

In the former, at best the voltage source does not contribute. The current source acts like the only source. In the latter, the voltage source is the only effective source.
 
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