@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.

@tomleslie Actually, I plotted a line graph for nusselt number and try to view that graph in 3-D view. I modified my sheet and still, there is output but I am not clear whether the 3D view has the same meaning as a line graph. Can you please explain why you used this f := transform((X, Y) -> [X, 0.5, Y]):

help.mw

@mmcdara I found your answer and read it too and it seems good but  I solved my ODE by using another method(series solution) and then combining. I accepted my mistake and if  you accept my fault then the response to my query. 

@tomleslie Thank you sir for your help. Would you please suggest some bok which have maple codes for ODEs and PDEs? last change.....Is it possible to generate or write loop at the end for an error table between numeric and analytic solutions? 

The value I am interested to use is We=0.1, Br=0.3,x=0, k=0.1, Q=00.5617, and lambda=0.0095.

Table as a reference or example

@tomleslie How to copy long expressions from one maple worksheet to other? Actually, when I copy my analytic solution from one maple sheet to another it misses some terms which is why the solution is not justifying each other.

Now I pasted the whole expression and the sheet is running successfully but the compression graph is not displaying.

Pls have worksheet

plots_New.mw

I deleted that file due to some wrong information in the worksheet that I uploaded. I am correcting my worksheet and the reupload my questions

@mmcdara Thank you for your reply. actually, I want to draw the graph for 3 different values of k as I mentioned in my original worksheet. Besides this, is it possible we label only two independent variable like u and y in the graph, not the third one? 

@tomleslie  Thank you Professor, can you please send me you email?

@tomleslie 

sir it seem little bit ok but I am afraid from the title of each plot that in ist plot you used the value of k=0.1,0.3,0.5,0.7,0.9 but the value of Q=0.1645 and lambda=0.0096 means that just changes the value of k but Q and lamda remain fixed??

similarly in second plot for k=0.1,0.3,0.5,0.7,0.9 and the value of Q=0.4392 and lambda=0.0093. while in both case, fixed the value of We=0.1, Br=0.3 and x=0.

The Idea that I want to apply here  is 

for k=0.1, the corresponding value of Q=0.5617 and lambda=0.0096, k=0.3 the corresponding value of Q=0.4392 and lambda=0.0010, for k=0.5 the corresponding value of Q=0.2564 and lambd=0.0093, for k=0.7 the corresponding value Q=0.1645 and lambda=0.0075, and for k=0.9, the corresponding value of Q=0.0659 and lambda=0.0031.

So, these 5 curve want to plot in one plot. Beside the value of We=0.1, Br=0.3 and x=0 remain fixed.

Sir, can you please add little explaination of the code to understand it.

Hopefully, I cleared the idea that i want to plot and thanks alot your help.