happilly, its works you can see...
can we find the value of r where the graph of P is zero i.e. P(r)=0, in the 2nd ode of dp/dr. 

also is the last command is true for the relation between P(r) and rho(r). i.e the graph of P(r) vs rho(r) where P as y-axis and rho as x-axis.
coupled_IVP.mw

right_file.mw 

please see at the given file whatever the signature but if I assign the indices ~i form ~0,~1,~2,~3 it does not display the value of christoffel symbol.

A lot of efforts I performed to obtained the right results, somehow I remain sucessful but the results are not exactly same as expected. I request you to kindly see at the christoffel symbol. I also sent the right results.

some_mistakes_in_christoffel.mw

you can see the right results in the given below attachment

right_christoffel_symbols.pdf

as you can comprare the results of both file.

thanks

I could add two equations (10)+(11) as mention in the guide of Physics(Riemann)(you told). since I am not expert in maple therefore I simply write (10)+(11) but the programme call them as simple number not the equations and the result is 21. I asked to you please learn me  write way of writing  equation (10) + (11) so I can compute Riemann.

see in the attached file, you may also see in at physics riemann at line 12.

@Kitonum the graph is expectedly write but i donot perform on my maple file.either u sent your maple file or to remove the error in my file.thanks

error_in_plot.mw

@Kitonum thanks,it works

but would you please tell me what is meant by TOV[5]... i couldn't undestand why did you wrote [5].

@Preben Alsholm hmm

would you please tell me how to write in a one pack like you write

sol := dsolve(newsys union ics, numeric,method=rosenbrock, range = ep .. 2*10^6);
plots:-odeplot(sol,[r,rho(r)],ep..2*10^6,thickness=3);
plots:-odeplot(sol,[r,m(r)],ep..2*10^6);
plots:-odeplot(sol,[r,P(r)],ep..2*10^6);
plots:-odeplot(sol,[r,v(r)],ep..2*10^6);

i just know to write one after the other command with > sign.

@Preben Alsholm the given code generates singularity error

i have been apply my code (in file) several time but it doesn't generate error such

@tomleslie 

you got the write answer!

is it possible to add more equation in this code, i try to add more equations but i could understand how did you write

one after the other with out using  >

 i want to add more equations coupled with these equations given in maple file.

i attached the file in wich equation of M(r) and rho(r) is given

odeProb2.mw

plots:-odeplot(sol1, [r, M(r)], r = 0 .. 1014030);

plots:-odeplot(sol1, [r, rho(r)], r = 0 .. 1014030);
but not understanding of way of writing....

@J4James 

here the only variable is r so v is a function of r. i.e v(r).

graph_of_exp_form_of_v(r).mw

@Kitonum hmmm

@Kitonum 

can't maple solve int with constant.

why did u took another equation u(x) also the condtion u(R) = 0

@dharr 

yeah! the write thing you obtained.

can we find the value of y(x) for which x =0 with out analysing the result of graph i.e by a maple command.

also I need only postive values of y and x so as I specify the range of x =0..2e6. i found nothing but only x and y axis.

@Markiyan Hirnyk 

this may be the pressure of star having high densities and pressure

@tomleslie 

i show you my solution.

but in this i am understanding what command i  should use to obtained the value where P(r)=0.analysing on graph is show the value of r where P(r)=0 is about 1334563....(some thing like). but is there any particle command of maple that directly evaluate the value of r for P(r)=0