@tomleslie sir I have repleaced the expression and now want to find the value lambda after puting P=0 by varing k in interval [0.1,0.9 ] by fixing R and B and repeat the steps for R and B. I find value one by one but its take alot of time; i want to calculate in loop. I try your previou suggestion in this file but could not get the answers.

k_and_roots.mw

@tomleslie  thank you for help. sir let me recheck my expression

@tomleslie here is my try to improve the quality or dpi of the graph.is it possible to increse more quality. Sir one thiing more, I used subs to show different graphs in one diagram is their any other way to do same thing.

Qaulity.mw

desire mean how to adjust DPI of graph like 300, 400 and 600 etc

@acer thank you sir. I was using diff tutor() to see the step but this way is more convient then that.

@acer can you please share some link from where i can download books related to thesis method to learn coding.

@acer I have observed the outcomes

@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