@acer sir thank you for your response. I have already solve by using this command but i need to show full step as shown in the book to my students. I have share two examples of these two method in my question. Sir if their is issue in figure means bluer can i upload again?

@acer  I have updated my maple to the 2022 version, and thank you for your help.

@AmirHosein Sadeghimanesh i have go through this command but it is mot working for all like to view step of solution of quadratic equation 

@Mariusz Iwaniuk do you provide paid services for coding?

@tomleslie  Thanks alot

@tomleslie firstly thanks alot for kind help. I almost done with my problem with your alot help through this maple forum. I mention the values of Q and lambda in attached analytic solution.

As you said this was your last changes into this question. but  I am  requesting you kindly change last change that is fixed the exact value of Q and lmbda instead of method of optimizer to determine you used..

The value of Q and lambda are K=.1, Q=0.5516, lambda=-0.0041

                                                  K=0.2, Q=0.4903, lambda=-0.0044

                                                  K=.3, Q=0.4290, lambda=-0.0045.

@tomleslie here is my manual solution and its graph. In my solution their is two parameter like Q and lambda.  I want to check the effect of k for fixed we=0.1 at x=0,0.5 for the rage of y=-1..1 and -1.125..1.125 and then repeat the process for different values of we and fixed value of k and then compare this analytic solution with numeric solution through graph and tables.

Note:  I have th different  values of Q and lambda for each k=0.1,0.2..0.9 and for we=0.1,0.2,0.3....0.9 the selected values of Q and lambda are given in plot command but draw at k=0.1,0.3,0.5,0.7,0.9 and we=0.1,0.3,0.5.0.7,0.9. 

Analytic_graph.mw

I am looking this type of grapg.(its only for refernce)

@tomleslie did you find maple sheet

@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