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Question 1: How do we solve Linear Time-variant systems?

Question 2: How do we solve Linear Time-invariant systems?

Question 3: How do we solve Non-Linear Time-variant systems?

Question 4: How do we solve Non-Linear Time-invariant systems?

I only know answer to the second question but I still want you guys to answer it for me.

(Answer is Laplace transform(continuous signals), Z-transform(discrete signals)).

Thank you for your time...