I just came to this note
For any LTI system the transfer function is W(s)=X(s)/F(s)
e.g for the system x' + 3x = f(t),
the transfer function is W=1/3+s
but this system has a term f(t) dependent on t so it shouldn't be autonomous, right?
2026-03-25 15:58:16.1774454296
Is this equation time-invariant and autonomous?
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Your system is time-invariant since the parameters (e.g. the number 3 that multiplies the x) do not depend on time. The variables (x,f) can depend on time.