[?] Decouple the differential equations by using Dsolve?

Questions
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1

I have to two differential equations and I want to decouple it by using Dsolve but not getting my required results. Anyone can help it will be very appreciated. Kindly see the attached file.

2

Maybe this helps. See attached file.

Regards, Mariusz

3

I hope this helps.

Regards HD

4

Thanks for your help. I got my results

5

thanks for your details concept. I have solved my equations.

6

I have two equations but different functions. I tried to solve it same, but could not get the simplified answer. Can you help me? and check where I am wrong.

Thanks in advance,

7

You demand the impossible. If FullSimplifycommand can’t better simplifying then no one will do it better.

8

Ok thanks, I will try another way.

9

Hi. You are lucky. The method I suggested earlier works in this case too, although the computations take a very long time indeed. So before running the attached notebook have a close look at it or better make a copy for reading.
Be aware that it is luck that DSolve works in this complicated case as well. It could well be that you have to use NDSolve for finding U and then Z in practical problems.

10

Thanks a lot for your suggestion. I have just solved according to your method and I found my results.