@Markiyan Hirnyk Do this command work for Maple 14?When I use it, an error occured

> restart;
> X := Vector([3, 4, 5, 6, 7]);
> Y := Vector([7.42494922444550, 3.67768248674133, 2.52235142453921, 1.95610223891559, 1.61770309810016]); DirectSearch:-DataFit(a/(x-b)^c, X, Y, x, method = cdos);
Error, `DirectSearch` does not evaluate to a module

> f := eval(a/(x-b)^c, [a = 5.78576581311883, b = 2.26189352728646, c = .821557593710752]);

> fplot := plot(f, x = 2 .. 8);
> ptplot := plot(X, Y, style = point, symbolsize = 20, color = blue, symbol = solidcircle);
> plots:-display([fplot, ptplot]);

@Kitonum How did you get the equation a/(x-2)^0.94...is it the equation for the point?Did you get it by using Maple?

@Preben Alsholm Thank you very much

@Kitonum Thank you very much..

@Carl Love "*F" means multiply with F. What is the meaning of this error....

@Carl Love ...

Yes...gamma is a constant. Its ok...but can you help  me with this error:

> for k from 0 to m+2 do

F[k]:=-1/(2)*(k+1)*H[k+1]:

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)!:

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

T[k+2]:=P*(sum((k-r+1)*H[r]*T[k-r+1],r=0..k)-M*E[c]*sum(F[r]*F[k-r],r=0..k)-M*E[c]*sum(G[r]*G[k-r],r=0..k)-E[c]*sum((r+1)*(k-r+1)*G[r+1]*G[k-r+1],r=0..k)-(D[u]*(k+1)*(k+2)*W[r+2]))*k!/(k+2)!:

W[k+2]:=S[c]*(sum( (k-r+1)*H[k]*W[k-r+1],r=0..k)-S[r]*(k+1)*(k+2)*T[k+2])*k!/(k+2)!: od: ;

Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object *F", Typesetting:-merror("Got internal

Please respond me by email, thanks.

tranx_hikaru@yahoo.com

Thanks @Carl Love...

I did get the same results as yours. However, the results are totally different from the paper that I am referring to. I would like to know whether Maple14 can help me to transform the ODEs using the Differential Transform Method (DTM). The ODEs (1)-(2) are as follows including the boundary conditions (3)-(4)..

f'''+ff''+1-f'^2=0            (1)

1/Pr(θ˝) + fθ́ = 0           (2)

f(0) = 0, f́(0) = ε, θ́(0) = –γ(1 + θ(0))           (3)

f́(η) → 1, θ(η) → 0 as η → ∞,                        (4)

I need to apply DTM to equations (1)-(4). After I've transformed these equations, I need to use the Pade approximation to solve these problem since the boundary conditions is an unbounded domain. 

Can you help me to solve this using Maple?