@dharr as shown in graph maybe letter are different,

you have this series Eq(6) which in my file is F and it is equal to ode solution  U(xi), i have to take derivative from eq(6) which is diff(U(xi),xi), if watch the equation after taking derivative you will see we have substitution which we can replace diff(G(xi),xi) after replacing  we have to find diff(U(xi),xi$2) becuase our ode contain U,U', and U'', but in my equation is just U,U'',

extra note: when we do some extra thing with eq(5) like diff(G(xi),xi)=sqrt(r^2*G(xi)^2*(a + b*G(xi) + l*G(xi)^2)) if take another derivatve is is clearly  apear which contain diff(G(xi),xi) in denomenatore then it have in numerator then they will canel then we substitute the U,U',U'' then we can find system of equation based on G(xi) power the coeficent of G(xi)^i=0 they will be our system to solve the parameter contain in equation 6, if don't undrestand let me know

@dharr  @acer  my Question is a little bet more but i though if i can do this step the rest i will do by myself but i don't know How to replacing in next other really  iam sorry   i can't replace even i have this amazing code is a little bit confusing , this is first time this happen

A.mw

@dharr in fact i am looking forward to find a generation function and use a loop for test that generation function for finding solution for ode, if possible i am sure it is possible even if maple can't find them i don't have knowledge to write down the code but i have idea , becuase i saw a lot of ode which no any mathematical program can find but they tested manually by hand but if we do by generation function and take out that function which make ode zero, i will post a new question about this topic ofcurse we can start by small ode and small generation function 

@dharr all of that function i try more than 3 kind all of them make a problem and when i found parameter the parameter set of parameter are so few and didn't give me answer for this equation i think this way is not usefull for getting solution i will look for another equation, thank you dear Dr

@dharr i found he did this part 

@dharr in fact, this is first time i solve this  new equation, the other equation the monomial of them is not to much but in here is more than 10 , i learned this trick from another paper, which have a lot term he just say take coeficcent of thus, i say maybe this trick give me answer , also my other problem of mine i don't want find all parameter just thus which contain in (f), and when i do that it not found and just runing , i am looking for some pretty solution of this pde and really i don't know the true idea behind of this exactly,i want choose thus parameter which make my PDE zero,  also in file have two H function please delete the second one which have one derivative in right hand side

S11-Dr.D.mw

@dharr thank you so much ,

@dharr if i am  automatically not get explicit answer i have to make them which one of them which this take a time, no problem thanks so much 

@dharr Every time I read your answer to my question, it brightens my day.
 

@janhardo thank you you did a great job thank you so much

@dharr i don't know where is should add print function u in loop, becuase i have to latex the outcome of u i have do it by hand  but if loop do it it will be amazing, also i need just thus parameter which contain in f (L2), is not different if have thus extra parameter but i don't know why my code not answer is not work when i write solve (L2,{a[1]-a[11]), also if have explicit option it will be great
thanks a lot 

trail-pdetest1.mw

@dharr So you say first i have to check in F1, then substitute in H then pde, that is also true, but i asked a new question related this a hour before, i try  some of this variable all of them not make my pde to zero but some of them do, i want seperate them at there , also if possible in ans[] just find that parameter which belong to our auxiliary function in L2

@janhardo  like that don't have problem but i have to change it by hand all of thus F to f

@dharr  i get exactly bilinear form of that is that like i say need the derivative and i found it , but why when i replace my parameter is not  give me pdetest zero, i try to find parameter a[1]-a[11] alone without other parameter , but didn't give me answer like paper did it , you are so good at finding parameter can you check it please 

Download test.mw

@janhardo can you change the letter F to f (capital to small) becuase i have to copy past equation i  needed also for G to g