@dharr i Hope you don't be mad at me about last my question which you said i can't help you , the solving question didn't have any issue but just constructing equations are difficult by hand instead of making them one by one by hand i try to say there is any way for construct them by code automatically ,
thanks again

@janhardo  have a trick for solving, and we have to do odetest for each solution to satisfy ode

@Alfred_F this method is new , it is easy but need a undrestanding, because this all solution must satisfy the ode, i hope some one undrestand and give me a good solution

@dharr @mmcdara  

Please don’t make it sound like you’re doing me a favor as a burden. I truly appreciate your efforts and the help with the code, but the way it's being said makes it seem like I did something wrong on purpose , which I definitely didn’t.
The code I shared was from an older version. I only modified it where I thought it was necessary. I’ve been working on a new equation, and since the structure was similar, I assumed it wouldn’t make much of a difference , just the equation itself was new.
I couldn’t have known that a small change would be considered so significant. At the end of the day, the core idea remains the same, and if someone is experienced in the work, they’ll easily recognize that.

betwen this file and sys there is not different just ode equation is different the idea it same 

old-orginal.mw

@Alfred_F i try to figure out but i don't have idea about this 

@dharr i am looking for make a system of coefficient of that term I mentioned before, then i solved that system for finding parameter involved in U(xi)  which make my ode zero.

@mmcdara you did your help in best shape you can, thanks you.

@mmcdara i want to do this, i want make thus equation eq0-eq6 find the parameter involving with G for get my ode zero  i want do systematically make thus eq like you did but i can't use and change your code is hard a little bit  for me

please see sys.mw

@dharr i want factoring [1/G')^i and  (G'/G)*(1/G')^i i want factoring this two term the second one is  together  in equaation G , i just write thus system in below for more undrestanding which i did it by hand one by one by copy paste in each coeffecent this is a little bit hard each time i do that i want do systematically

@dharr it is different from the other  and i think it is not apply that factoring  in here we have two multiply term in last one we have just one 

@dharr in last of each equation i write this equation come from what in fact i have to factoring   like that , i don't want factor eq i want factoring G1, in last of each equation i have coeffecent of that term 

and this is come from this series 

@dharr amazing, is not my fault sorry ,i did my best try but each time need your hand to go on....thank you Dr

@dharr it work thanks dear dctor 

@dharr i thought i can hundle other step really i did samething but is not apply for general form , i did the samething but not apply i want solve ode  but becuase the step are too long i just ask where i stuck otherwise i will upload all, like this

@dharr is nonsense is just becuase sign of case instead of this {} i write this [] , thanks dear dctor i will upadte my old code , and referesh all, thanks a lot Dr dctor david