Hello,
I am trying to solve a system of differential equations as below
Unfortunately it takes too long and puts a lot of strain on the computer. Could someone advise me how to do it to make it optimal. Maybe one of you could try to solve this problem on your computer?
Kind regards
Marcin
ukl_row_roz_rozw.nb (3.38 KB)
In fact, this system of equations cannot be solved using Mathematica.
Maple 2022.2 can solve, but you won’t like the answer.
See attached PDF file.
Diff equation.pdf (1.35 MB)
I didn’t like the hint 
I need a close/analytical solution. Thank you for your interest.
Many ODEs do not have symbolic solutions in terms of commonly defined functions. The ODE in the question probably falls in that category. However, it should be noted that DSolve sometimes is unable to solve ODEs that do have symbolic solutions in terms of commonly defined functions.
If I manage to solve the problem I will let you know I will do it maybe in a slightly different/engineering way not directly but I will do it strict.