@acer Why are your exponents off by 4 decimal places compared to the OP's?

@toandhsp Did you get no result, or did you get a RootOf result? If the latter, add the explicit option to the command:

solve({30+1144*r^4-832*r^2=0, r>0}, explicit);

@ctnaz I know that *F means multiply by F, but you have "*F" not *F. What is the purpose of the quotation marks?

@Preben Alsholm

Saying the same thing differently, in a way that seems clearer to me: Reading the file with read is equivalent to executing b:= 2*z at the global level, regardless of where the read statement is placed.

I recall reading this in a help file, but I can't find it at ?read or ?parse. Preben, can you find it in help?

I also believe that reading a text file (as opposed to a .m file) with read is equivalent to applying parse to the file's contents, but I can't find this in help.

Indeed, MaplePrimes should have a rule that you need a certain level of reputation in order to Edit Questions after they have Answers!

@Markiyan Hirnyk It can't be a comment to your Answer because I wrote it before reading your Answer.

@Markiyan Hirnyk I show that erf(10.) is the source of the problem and that the erroneous value is exactly 100*sqrt(Pi). I also show the value of using exact arithmetic from the very start.

@acer In particular, you've changed the range of r from 2.5..4 to 0..0.4 and the range of x from 0..1 to 0..2. How did you know exactly how to change them?

@emmantop Your file didn't upload properly. Can you try uploading again?

Maple is saying that you need two more initial conditions. Can you come up with two more?

@ctnaz Your code contains this line, which makes no sense to me:

F[k+2]:=( sum(F[r]"*F"[k-r],r=0..k)+sum(G[r]*G[k-r],r=0..k)+sum((k-r+1)*H[r]*F[k-r+1],r=0..k)+M*F[k])*k!/(k+2)!:

What is the "*F" supposed to mean?

@adel-00 The symbolic commands maximize and minimize won't work in this case because the function is given implicitly. On the other hand, the commands in the Optimization package work numerically and will accept constraints.

@Markiyan Hirnyk Oh, I missed that. You're right. Sorry.

@Markiyan Hirnyk The point returned by Optimization:-Maximize does not correspond with the local maximum shown on the graph. The point returned by Minimize looks okay.

Could you please attach a worksheet with your code?