Linear/Nonlinear, time-variant/invariant systems

[pairofstrings]

Hi guys. I am super excited to know answers of the questions that I am going to write below and want you to give me only the gist or a superficial information on the concepts and hopefully I will find the rest of the matter by-myself.

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...

 

[smk037]

These are very broad questions...

 

[pairofstrings]

These are very broad questions...

I don't want you to explain me the entire concepts. I only want one word answer. Like I answered my 'Question2'... I only want to know name of the maths concepts that will help me solve these systems. Like I answered 'Laplace transform and Z-transform' to my 'Question 2'. Likewise, can anyone answer my questions in a very terse manner. Just the name of the maths concept will do.. I tried looking on the internet but I got confused... Help please.

 

[DragonPetter]

non-linear can be done with piece-wise/condition-wise, small-signal approximation, or with simulation

obviously laplace/fourier do not work alone in non-linear analysis.