@vv Thank you! But now I have a new problem: in the output of "sort", the non-integer powers of t are replaced by combination of sign and abs, for example t^(41/7) by signum(t)^41*abs(t)^(41/7). Do you know how to avoid this?..

Thanks a lot!          

Thank you very much!

@Kitonum Thank you, but what if I have a recurrence of higher order, whose characteristic equation it won't be able to solve?..

@Markiyan Hirnyk 

Yes, indeed. Then in order to see the plots again, I have to execute all the commands line by line, and then everything is OK. I didn't know how to see animations, but here the answer from Christopher2222 was exactly that I needed.

@Christopher2222 

Indeed :)

Many thanks!

@Markiyan Hirnyk 

Thank you for the answer. I ran you file and I observe the following.

First, if I just execute it line by line, I still have the same problem. I executed all the "regular" lines by the "!" button, or by the Enter key, and for each code button, I did right-click -> Ececute code. So I don't understand what I miss. 

If I first press "!!!" it behaves better - I see actual plots. However, all the output is immediately replaced by a message "output redirected". I don't know how to handle it. If I try to execute the commands that produce plots after that, it shows them reasonably, so the initial problem seems to be solved. However, still I don't really see animations: the commands that are supposed to produce animations, show a single plot.

Could you, please, help me with these issues?