@dharr  can you make construct system of equation just by x^i and t^j other like x*t =0 just count the power x and t seperatly if we do that iam sure thus parameter must be come out

@dharr I did the same like in paper did but I don't know why our parameter is different , I don't know how I do this stuck badly , and this is easiest one in comparing to other equations 

@dharr thanks for answer Dear Dr.David
i look in a lot paper they didn't explain how they reach the solution  but in some paper they collect the coefficent  of x^2,t^2,x,t, if have more than one dimension is like that x^2,y^2,t^2,xy,xt,x,y,t after all  i have to find a way for find this kind of parameter so how they did it, picture one is our equation can you find thus parameter already shown

like thus picture below

@acer i try work on it and somehow i fixed but really i don't know how this work just watch and if undrestand tell me

tester.mw

@acer this is will be distroy the whole my file in latex and i have to rewrite all this is a part of it

@acer it is so clear for me, i want find parameter   A[0],A[1], and B[0]  and any other in complex equation  and substitute thus  parameter in S which this S=U(xi) i want replace U(xi) in Fode it must satisfy  Fode=0.

@acer  i want find coiffecient i want something like that (ad+gh)x^2+(e+t)x+... i wakt find equation and find parameter amd change parameters 

@dharr  Dear Dr
 so i can't graph with three variable x,y,t at same graph and give them range i must act with two of them and other must be free variable or what becuase i fixed but i act with y like free variable ?

@acer  do you mean we can't plot with two or more parameter for graphing so i got this mean from your comment  y and x or x and t or y and t must get range of variable otherwise must be free ?  becuase i graphed like that but i want  give range to y too so is possible or not? i must act with two of them ?

@acer this code is yours you know how arrange things this equation and solution are (2+1) dimension so  x and y and t which is time are are used like a range other parameter are free in M

@janhardo i think is wrong, i am looking for parameter alpha[0],alpha[1],beta[0] must find with one or more  parameter in the equation  at least one or two of them

@acer you did a great job but why forget a code for finding the parameter automaticaly at the matrices, i didn't know where i should rename and say find thus parameter if you do that it will be so good and if you do odetest like this stuff just you can do it will be ultra hight level code

@dharr  watch you will get  full notion

collect_by_hand.mw

i don't know why my parameter not coming out is ok if add more parameter or reduced them with this condition each parameter of  equation must not be zero 

@dharr Hi dear Dr.David
i am glad to have your response again, in fact i want  in (G1) we have some function term and other are parameter like 1/G(xi)*($$$$$$$$$$$$+diff(G(xi),xi)(##########) we have something like that i want collect 1/G(xi)*diff(G(xi),xi)/G(xi) then finding term i must do this by hande if there is no any code for get the solution of our ODE, i did collect almost but how i can arrange them by code automaticaly not use any hande, this code in eqs are used is useful for some function with one term i wanna know is work for this kind of function too or not?

@janhardo  thanks i will do another post soon i am work in simple equation  in laplace i will try do this stuff of adomian by integral is old way but it is work for me , also have a lot step  try your best if finish upload mw