@dharr  I’m always interested in your code; it consistently brings something new and exciting, especially in the final lines!,

@dharr i didn't put my case1 in L1 equation which is our ODE  i did and i get correct solution

@dharr I've been trying, but I keep getting confused. It's the same thing every time—factoring gives me trouble. I've been working on fixing it, but I'm still struggling. There are also a few simple solutions for such PDEs, and if I can tackle all of them with your help, it would be a great achievement!.

Dr.David_1.mw

@dharr I'm truly proud of you, Dr. David! I was stuck on this problem for an entire month, despite reading at least 100 papers, but I just couldn’t solve it. You did it, and I’m incredibly grateful. Now, I need to understand the code so I can tackle similar problems in the future. If I have any questions, I’ll be sure to ask. Thank you so much—I owe you more than words can express!

@acer my question is this my sign of integral not remove and don't do work when i say take integral from all equation! in fact i am looking for finding parameter there is no any explamation in %99 percentage of paper for finding i did that becuase i want try this too to take intergal at each term then looking for it  my question is so complicated i am looking for answer just which is i not even close to it
please tell mapleplrime moderator don't delete my question till i get my answer after i get my answer i will delete them all by myself

@dharr  this another paper just one term add but he say for collecting term 

@dharr can I have thus code for arrange the equation I want try more 

@dharr I don't know shape of equations, I don't know how arranged them, but it's idea must be like that coifecent of x^i and t^j and also maybe contain x^0t^0 it mean constant other must zero but results must be this if  we find this we will figure out what we have to do in future equations 

we look for this 

@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