@acer 

Thank you for your solution.

@nm 

Just what I wanted, thank you.

@acer 

excellent explanation and work, vote up from me.

@rcorless 

thank you for the files, very interesting.

@rcorless

Saw code for modeq in your 1997 paper. Is code available for download, does it work for recent maple.

Thank you.

maybe use sed to change , to . before input like

sed -e "s/,/./g" inputfile > outputfile

then read outfile in maple

@lcz 
 

in this case use the read command inside maple, see help

@lcz 

windows doesn't know that this is a maple input file and gets confused. you must run maple as I described with the name of the input file you want to process. 

@Brian P Hanley 

Not sure but the matrix should be gone after M:=evaln(M) if I understand evaln correctly. 

Could also try

M:=unassign('M'); 

Help system on unassign gives matrix as example.

@The function 

I answered the question you gave and believe thats the answer the book wanted, @vv and @Carl Love can debate the problem with different values of the matrix A.

@ecterrab 

Yes Im looking at inverse problem and jets has a simple command for this (lagrangian) and automatically checks Helmholtz conditions and gives error if they are not satisfied as expected. I just cant work out the syntax of the command. Since this is what I must study I will continue to try different syntax till it works.

Thank you.

@ecterrab 

Thank you for comments. I loked at CalculusOfVariations, it works our E-L equation like variation command in jets. It doesn't do inverse problem like lagrangian command in  jets.

JetCalculus package also does E-L equation but not inverse problem.

I think this is a correct summary.

@Rouben Rostamian  

Thank you, thats great.

@vv 

Thank you for the comment. I will rethink this.