@janhardo here 

@janhardo k is range instead of l in first picture

@janhardo i want plot w in second picture write in simple shape and you can change  other parameter too for example first picture  change parameter in first (a) then another picture k and so on in each one of them somethng will happen

@janhardo can you use your Ai for ploting this for me ?  i want like second picture, instead of m you have w in picture one

@janhardo this is don't have any different from mine . it is same . but is wrong, and i don't have any time for waiting i have to answer this until night , this is easy example mine is further hard.

@janhardo I have to find it 

@janhardo  i need the code for solving other steb by step, my code not working they stuck

@janhardo i am  looking for finding how he reach this achievment becuase my pdf is different from this but how seperate how find coeffiecent this is importan for me ...

@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.