thanks ever so much

thank you

works perfect. thank you so much for all your help

thanks for the help. I tried with(LinearAlgebra) -  unfortunately it still doesnt work with either matrix or Matrix.

Right here is my maple worksheet. I'm getting very frustrated with the matrix at the end. I want it to transpose but it just wont do what i want. any ideas?

restart;
with(plots);
nmax:=14:
Order:=nmax+1:
de:=diff(F(eta,R),eta$4)-R*(diff(F(eta,R),eta)*diff(F(eta,R),eta$2)-F(eta,R)*diff(F(eta,R),eta$3));
series(eval(de,F(eta,R)=add(F[k](eta)*R^k,k=0..nmax)),R):
des:=[seq(coeff(%,R,k),k=0..nmax)]:
bcs:=k->(F[k](-1)=`if`(k=0,-1,0),F[k](1)=`if`(k=0,1,0),D(F[k])(-1)=0,D(F[k])(1)=0);
for k from 1 to nmax+1 do
    F[k-1]:=unapply(rhs(dsolve({des[k],bcs(k-1)})),eta);
end do:
plot([eval(diff(add(F[k](eta)*R^k,k=0..5),eta$2),eta=1),
       eval(diff(add(F[k](eta)*R^k,k=0..10),eta$2),eta=1),
       eval(diff(add(F[k](eta)*R^k,k=0..13),eta$2),eta=1),
       eval(diff(add(F[k](eta)*R^k,k=0..nmax),eta$2),eta=1)],
       R=-20..20,-20..20);
plot([eval(diff(add(F[k](eta)*R^k,k=0..nmax),eta),R=1),
       eval(diff(add(F[k](eta)*R^k,k=0..nmax),eta),R=17),
       eval(diff(add(F[k](eta)*R^k,k=0..nmax),eta),R=18),
       eval(diff(add(F[k](eta)*R^k,k=0..nmax),eta),R=20)],eta=-1..1);
D2F:=eval(diff(add(F[k](eta)*R^k,k=0..nmax),eta$2),eta=1):
DF:=eval(diff(add(F[k](eta)*R^k,k=0..nmax),eta),eta=0):
c1 := [n,$0..nmax]:
c2 := [a[n],coeff(D2F,R,t)$t=0..nmax]:
c3 := [b[n],coeff(DF,R,t)$t=0..nmax]:
Transpose(matrix([c1,c2,c3]));

yeah i did notice that. thaks for the help :-)

thanks thats a great help. ive used doug's code. how would i adapt this to add another column?

how would i go about revising my problem so that Maple responds with floating point coefficients?

is it possible that the fractions its using are so small it just takes them as 0 from 15 onwards?

do you think there might be a better way of writing this to avoid the problem?

just realised that there is a mistake. where is says:

"Extract the individual equations for each power upto R^5"

it should say R^15. doesnt affect the program but thought I would correct myself

thank you very much

thanks very much. that was a big help. I understand how this works but there is one part i don't understand. would you mind explaining it to me please?

for k from 1 to 6 do
   f[k-1]:= unapply(rhs(dsolve({des[k],bc(k-1)})),s)
end do;

in this for loop what does the unapply do? this is the only section i was confused on.

thanks

mj