@tomleslie  sir I have solved this non linear ode manually and find its zero order and ist order solution like as series solution or called perturbation solution. Then I combined these solution and plots graph for u against y. i am trying to convert it into maple sheet but facing difficulty. The main task is to validate this analytical solution with numeric results  in same graph and in tabular form at x=0 and x=5 for differnt values of k and wi as like the examples you give in odelot5 maple sheet. In table is it possible to a column of  error for  analytic and numeric solution.

 Analytic_solution_for_comp.mw

@tomleslie sir iirst all sorry. Actually when i send my workshet to my teacher, He suggested next step to doo. I am try to make separate separate maple sheet for k and wi, I made separate sheet for k but when i try for wi the results are not genrtaed. Can you please fixed the issue.

1- my tecacher suggested when i draw graph for  differenet value of wi and fixe value of k=0.1 and x=0 the range for y=-1..1

2-my tecacher suggested when i draw graph for  differenet value of wi and fixe value of k=0.1 and x=0.5 the range for y=-1.125..1.125

And is it possible to make complaresion of both soultion analytic and numerical by using table and graph?

this my try for separate sheet help_solution_11-03-22.mw 

@tomleslie Thanks sir

@tomleslie sir In My first question i upload the  graph of my analytical solution in maple worksheet and in which i draw the graph at the value of k=0.1,0,3,0.5,07,0.9 so i am interested to compare my analytical solution with numeric graph at the same points. 
2- secondly i upload a worksheet of FDM algorithm and in question statemnet i clealry mentioned that the algorithem is working with adjusting thr range of y but i am interested to fixed the range of y=-1..1. 
atlast as you give me last chance to clear  my question, 

Actually i want to compare my analytic solution and numeric solution  in both way e.;g through graph by vering ka and wi and in tabular form.(analytic solution and numerical solution)

@tomleslie thank you for your help. The worksheet is working according to desire. I am trying to changes the the range for input variable but failed. 

1-  Sir the code you have upload Odeplots2 by using built in FDM is working good but one thing i am trying to changed in it but got syntex error. I want to show the effect of  k=0.1,0.3,0.5,0.7,0.9  on graph and similarly for wi=0.1,0.3,0.5,0.7,0.9 on graph and in legend. sir kindly  

odeplots2.mw.

2. The problem for FDM file was that when i fixed range for y=-1..1 in plot commondm i received sutex eroor but when i removed the range i received graphg so i was interested to fixed range for y that is was y=-1..1. sir if possible kindly fixed the range for y=-1..1 in odeplots3. 

odeplots3.mw

@Joe Riel  I have try but failed

@tomleslie Thanks alot 

@mmcdara i have my code in mathematica and was trying to upload but failed and then i converted into pdf nd upload here. I am only interested to convert above file in maple

@tomleslie  I am trying to solved same problem by using FDM but got error when i fixed the ranfe for y=-1..1. \but whgen i removed the range of y, i received the results but its different then the analytixcal result. Can you please chck where is the problem.

work_new.mw

@tomleslie Thanks alot, it is working according to wish. Actually i need to write detail about the method which i have used to solve this non linear DE. can you please guide which method you have implemented? Can you please help me to ad numeric table for u as well. I am trying to solve this problem form a coulpe of month but could not get fruitfull results. 

For reference: I am taking an idea from a paper in which author have used RK shooting method to solve nonlinear problem and the steps he followed. kindlay have a look at page 669 (11 / 19) of the atteched pdf file. looking for your help.

For_Reference.pdf 

@Mac Dude I do not have idea about this, i am trying manually but failed. could you please help me about conversion

@Preben Alsholm really sorry for syntex error. Actually this is my resarch problem. I am understanding your solution besides this can you help mw in mu worksheet. Is thier any book or pdf file from which i learn about maple? I am using maple 19 and soon will update my maple

@Preben Alsholm sir here is my try but could not get the result

Help_Numeric_solution.mw

@Preben Alsholm here is table for reference 

@Preben Alsholm the value of is h=1+x^2/2, actually I want to check the effect of beta (0.1,0.2...0.9) on velocity u through the graph by fixing p=2 and x=0 in the values of h and again for the same value of beta and p we suppose x=0.5 and draw the graph and also want to generate the numeric table of velocity. I have a paper in which they used the shooting method with rk45.