@mmcdara thanks sirfor your help

@mmcdara sir, I made change little bit in my expression but received error

Error.mw

@mmcdara thank you for response and help. Sir can you please add the detail specially this part

ymin, ymax := (min, max)(plottools:-getdata(p)[3][.., 2]):
eps   := 0.1:
Vline := plot([[0, ymin-eps], [0, ymax+eps]], color=black):
Hline := plot([[-5, 0], [5, 0]], color=black):

Left  := -4.8:
Right := -0.5:

Legend := plots:-display(
  plot(ymin, x=Left..Left+1, color=red)
  , plots:-textplot([Left+1, ymin, " N= 1, M= 1.3015"], align=right)
  , plottools:-rectangle([-4.9, ymin-eps], [-0.2, ymin+eps], color=white)
  #, plot([[Left-0.1, ymin-eps], [Right, ymin-eps], [Right, ymin+eps], [Left-0.1, ymin+eps], [Left-0.1, ymin-eps]], color=black)
):

Sir if, I want to change the position of vertical line then which values do i ned to change? Similary, if I want to add 4 or 5 legends then how to add or where to change?

sir if I want to show only legends then which portion do I need to mention in the code, please have look on my file

Help_graph_and_legends_place.mw

@mmcdara The shooting method is not necessary; if there is any other numeric method which we used to plot streamline by using the stream function, please help in this regard.

@mmcdara thanks sir, actually, I need to use this relation in another equation that is why i am inetersted purely in relation not specific solution.  Let me consider your suggestions.

Sir could please response to my this separate question which I asked fews days ago

https://www.mapleprimes.com/questions/236290-Whats-Wrong-With-My-Worksheet-Need-Assistance

@acer Actually, h=1+x^2, and I am interested purely in the relation between h and lambda by putting Eq=0. Once I get the relation, I will replace the value of h and will isolate x in terms of lambda and other parameters.
If it is not possible to develop a relation, then is it possible that we can suppose the value of T, something like T=0.2 or 0.5 and generate data points between x and lambda, then make a polynomial or relation between x and lambda?

@mmcdara sir it possible to solve my ODE numerically by using shooting method by considering stream function and then draw streem lines?  as reference or idea, I am uploading a picture. The information given in picture is not related to my problem, I am uploading just as a reference. Very thankful for help in this regrads?

@mmcdara although it looks little bit complex but it is working according to requirement. Thank you for your help

@mmcdara sir, I am attching a picture for refernce. I am interesting to write my ODEs look like written in the picture.

@mmcdara thanks sir for your response. My problem is ok if i fix the value of n such as 3,4,5 etc but I need ODEs with n  by considering different power of beta like 0,1,2,3,4.

@Joe Riel thanks, but I am interested to run with the value of y because in some graphs, I need to change range of y i.e. y=-2..2.

@gkokovidis thanks its working....the part above the example emain same for any other problem or we need to revise according to new problem?

@gkokovidis I have gone through this post. I am faceing issue regarding implemention on my worksheet.

@tomleslie sir, I am thinking about your suggestion about the accuracy of the built-in numeric method and re-calculating my analytic results to get good validations of both results.  Is there any other method in maple for BVP to compare these numeric results with them to check the accuracy or validity of this method by producing graphs and tables and then comparing these two numeric results with analytic results?

@tomleslie sir In Worksheet that i have uplaoded, used many these option and found from help. Few of them could not find.

i will resd again thanks for your suggestions but you do not guide me about DPI means how to preserve quality or increase DPI of graph by using maple?