Respected @tomleslie 

Thankyou for reply.

plot(eval(eq2, p), x = 0 .. 1, color = colors[j]) in the above code, but we need to evaluate f(x):=eval(f(x),p); for plot.

Dear  @Carl Love 

Thanks for the response.

Advances in the Homotopy Analysis Method book -pages-274-279 the author provides a complete procedure. 

I hope these images can provide a clear view of this analytical solution for ode problems.

Thanks for the support and waiting for replay.

Dear users
I have some doubts in the initial function(f[0](x)=1-exp(x)).
in the image equ 16 and equ 18 are the main functions.
how to insert that function in a program.

I am working on this model at present.
for a further process, I need this clarification.
thanks for the support and waiting for a reply. 

Dear @Carl Love 
Thanks for the reply.
I'm using maple 18. In that, it executing without error.

I apply the same code for another problem, I received a proper result.

But this problem guess is different : f[0](x):=1-x^(2);

above mentioned problem gusses were different.

Respected @tomleslie @Christian Wolinski

Thanks for the reply.

The results are looking good.

Respected @tomleslie  @Carl Love  @Christian Wolinski

finally, I got a result using the print comment.

Thanks for a healthy discussion.

Respected @Christian Wolinski 

previously using one for loop I used ba3 := [(X1 || (1 .. NN))(0)] comment to disply the  rhs(-R(0)[3]) value.

using two for-loop how to display the date :

eg:

Respected @Christian Wolinski 

how to display X1[i,j] value

Respected @tomleslie 

Any differential equation doesn't have a unique solution. Based on their initial guess solution will vary, sometimes may exist two or three solutions also. 

in Matlab, bvp4c was used to achieve the solutions with two different initial guesses. 

for first solution: solinit = bvpinit(linspace(0,infinity,100),[-1.50 0 -0.3 0.0 -0.3 0 0]);

Second solution: solinit = bvpinit(linspace(0,infinity,100),[-1.50 0 0.3 0.0 -0.3 0 0]);

JVBASHA.docxJVBASHA.txt

in the above metion text and word document have a matlab programme what i used, copy and pasete in matlab.

Have a good day.

Thank you,   @Kitonum  

Now it's working well. 

Has anyone got a solution for this FEM model?

Dear @tomleslie 

I am using maple18. shade between commend has not existed in this package. any alter way is there.

Have a good day.

odeProb2.mw

Error, shadebetween is not a command in the plots package
Error, (in plots:-display) expecting plot structure but received: plts

Dear @tomleslie 

Here eta in the boundary condition.
so, instead of eta, we will take only the limit value.

like: g(N)=f(N)+N*D(f)(N)-N*D(g)(N)

Have a good day.

Dear @tomleslie,

Thanks for your quick response, and also your clear explanation about the odeplot and shade between comment.

Dear @tomleslie,

Here N is the limit value.

eta(N) represent eta at N value.

I didn't get a clear idea, how to use or insert eta at the limit.

that's the way I noticed this