@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

@janhardo  i have other info too just ask what you need?
also there is another easy method if you can't do this i will ask anotehr question about taking adomian polynomial by intgral is easy for writing program i don't know writing program otherwise i will do i know each step by hand  but for programing i am not able to write now , but i will learn one day

@janhardo can you do for multiply or how you gonna make a prc just i change a function with subscript and the procedure work becuase thus example i want to solve are so complicate
can you construct the exact shape algorith becuase this ethod in top picture are so easy if you can write that it will be emazing

@janhardo please do by yourself i don't know where i put it in and upload file , i will distroy

@nm you did a great job, i wish i know your coding... beliave me when i watched your code i didn't know where you calculate relative error i didn't find it except division but didn't have a name....
i want add two other term if possible  each one alone like exact solution in one column aprroximate in one column and error in one column also relative error your code is high level i can't involve but i liked so much.
can you answer my other question it seems you can hundle them too ? i am waiting for each one of them

@janhardo  the zhao method is easy is so  easy with your coding you can write easily

@Alfred_F I like your information specially your link
if have any link about soliton solution give me the link

@janhardo this adomian but not in shape of top algorithm, how we apply this for the second example I have problem with this kind example  I  have problems with two one more variable , and make your outcome more prettier and be better if instead of results outcome be like this A[0]=@ next line A[1]=# so on