@Kitonum 

Thank you for the adjustment and your time. The suggestion is insightful.

One more thing! If I want the legends within the graph, how do I accomplish that?

Kind regards.

@acer 

Thank you so much. Your methodology is an eye opener.

Accept my best regard as always.

@tomleslie 

Kindly see the worksheet under my reply @ acer.

Thank you and kind regards

@acer 

Thank you for your reply. I wanted to write an independent code different from the Maple inbuilt package for numerical. However, met with difficulty. The exact and numerical in my code do not agree.

Kindly see the attached for your perusal and possible modifications and enlightenment
 

Download EULER_Correction.mw

.

@Kitonum 

Your suggestion is appreciated.

@acer 

Thank you. The different suggestions are appreciated.

@acer

Your suggestion is very useful. Thank you. It is appreciated.

However, I will appreciate it if I can learn some other ways to get the same effect from you.

Thank you and kind regards.

@Rouben Rostamian  

Thank you so much for your time. It is appreciated. Can you kindly include in the code the Matrix representation of the coefficients of the system of ODEs just immediately after " sys := { seq(eq__i, i=2..n-2) } union bc_left union bc_right: "? It would be appreciated. Thank you in anticipation of your positive response and best regards.

@acer Thank you so much. It is appreciated. 

Thank you it is appreciated

@Rouben Rostamian  

Your Suggestion is  highly apprciated. Thank you and kind regards

@acer Thank you very much. I really appreciate your suggestion and value the time you spent on it.

@Kitonum I really appreciate your suggestion. However, I have applied the "allvalues" command before settling for the line b the results dont just make any sense to me (too long and some contain imaginary) which shouldnt be.

@acer Thank you and kind regards

@acer 

Your suggestion and correction is appreciated . I have view questions as I am new to some of the command used in the correction

1. What is the function of

2. Is it possible to display the final resuts " all2 " one after the other as contained in the original code. i.e alpha[1],beta[0],beta[1],beta[2],gamma0,gamma1,gamma2 separately and on separate lines. Your suggestion will be highly appreciated.

Thank you and kind regards.