@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? 

@tomleslie sir thanks a lot for a lot of help every time.

@tomleslie  sir once I received the numeric solution then I am trying to generate a compression solution between analytic and numeric graphically and errors between them through the table. I plotted the Analytic solution but got an error in combining them I made some changes in your above sheet and tried to run my sheet but got the error. Can you please help with it too?

odeSols.mw

@tomleslie yes, I have been trying to solve this ODE for the last two months, either analytically or numerically, and I solved its analytical solution and sketched its line-style graph for u. Besides this also tried to make it a numeric code.

Now my teacher asked me to draw the phase portrait graph. Thank you for your suggestion about the singularity. The value of n can be changed or is supposed to be greater than one. We can suppose the value of n=2 or 3 or 5 etc. Is it possible to draw its phase portrait graph for n greater than 1, such as for 2,3 or 5? or you can adjust any possible value for parameters to draws required graph.

@tomleslie  I am attaching my ODE with the boundary condition.  This is the second-order ODE, and I explained the value of the involved parameters in the worksheet. is it possible to draw in my case because, in the above reply, you are asking about its order ODE or initial condition?

ODE.mw

@tomleslie  the purpose of the phase diagram that shows the qualitative behaviour of an autonomous ordinary differential equation in a single variable. In my case, I am uploading the solution means the velocity of my BVP problem, and I want to know whether its phase portrait behaviour is according to the geometry. For axes, I want to plot u along the vertical axis and y along the horizontal axis. The value of unknowns is given in my maple sheet you uploaded in response. I have plotted the line-style graphs for velocity but my mentor asked me to plot velocity in another style than line. As a reference, I am uploading a picture for the phase portrait graph. This picture is not related to my problem but just as a reference.

disp.mw

@tomleslie Thanks for your help.

@tomleslie Thanks sir.