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These are replies submitted by AHSAN

@Kitonum bundle of thanks sir by the way why we take eval(rhs(%), x = 1);? rhs stand for right-hand side or is there any other meaning and % meaning?

@Kitonum sir i am looking for how to find the value of lambda?

@Kitonum why it gives error

h := k - (k - 1)*x;
DE := diff(p(x), x) = 6/h^2 - 12*lambda/h^3;
             d                6              12 lambda    
      DE := --- p(x) = ---------------- - ----------------
             dx                       2                  3
                       (k - (k - 1) x)    (k - (k - 1) x) 
BC := p(0) = 0, p(1) = 0;
                    BC := p(0) = 0, p(1) = 0
simplify(dsolve({BC, DE}, p(x)));
Error, invalid input: simplify uses a 1st argument, s, which is missing

@Kitonum thanks sir, it is working well, i have confusion in the last step can you please explain how and why you did this

p:=unapply(eval(p(x),%), x);

and how to fine the value of lambda=k/1+k after integration

@Kitonum Thanks sir for your effort but i am looking for the solution which shows in the attached picture. first, need to put the value of h in the given first order ode and then solve obtained expression by using BCS that you b the same as p in the picture and neet to put the expression p=0 solve for lambda. but I do not obtained the exact value of p that is given papers

@Mariusz Iwaniuk pls have a look and required results

@Mariusz Iwaniuk that better idea can you please update the sheet that how could I generate the different graph in the same picture for different value of M=0.1----0.9 and for fix k=2 etc

@Mariusz Iwaniuk can you please give a little explanation that you did in the sheet and why you take rhs(sol)?

@Carl Love I have already solved this by using dsolve command now I am looking for the algorithm of FDM

@acer Thanks sir, it is working and your way of helping is always helpful for me. But i don't understand why you convert into EXP?

@vv sorry sir in the first file there was a mistake in expression. Still, at my pc, it is not giving result and not integrating, I do not know why?



@vv it is not working, can you please have a look on my try, pls have attached work


@Kitonum sir i already checked this link but could not succeed in my problem. i am sure that me doing in wrong way that is way i posted here for help.

@Kitonum thanks it is ok but can you please help me about the remaining questions pf my worksheet. There is other questions 2 and 3, pls help me to solve them

@Carl Love  i wrote thanks alot

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