@BrendanMcKay Thank you! If you copy/paste your first sentence to an answer, I will accept it. This is the answer I was looking for. I have to say I can understand your critique, I wasn't sure where to ask this question, and which tags to assign it. If you think it would be helpful for somebody else to edit the tags, please, do so, or suggest me how to do it.

I simply didn't know this before, this is the answer to my question. Thank you!

@Robert Israel I realize that this is the case and this fine for me. I would like to make experiments with such demonstration systems for introduction purposes.

@PiyushGrover They should be more complicated in the sense they reveal strengths and weaknesses of different ODE solvers. Another example may be 2nd order linear system with a large stiffness ratio and so on. I could take the time and try to enumerate them, but I am hoping to find a reference that already did something similar. This was already done in mentioned articles, but with local error as one of criteria instead of global error.