Not really a homework question but it's a rather basic one so I figured this would be the place to post it. It seems to me that any continuous time system in which the output depends on some time-derivative of the output (i.e. y(t) = x(t) + dy(t)/dt) cannot possibly be a time-invariant system. Am I correct in this assumption or am I missing something important?
A time invariant system is one where y(x(t),t-T)=y(x(t-T),t). In other words, a shift of T in the input signal causes a corresponding shift by T of the output signal. If my initial guess was correct then any continuous-time circuit with a capacitor or an inductor in it would not be time-invariant. I'm pretty sure that this is not the case but I can't seem to figure out the math to prove it. In fact when I do the math I can only disprove the time-invariance of a capacitor or inductor system. I must be doing something wrong but I can't figure out what it is.