Thanks for Jack'S and Bill's kind help. I can run some basic code mow.
While I still have some related problems.
Since I have solution near the r-> 0^+, and I still have some symmetry to set A_0=1, chi_0=0 and c_0=1, the only changing initial condition B_0 and q. That is in the following code...
Thanks for Bill's and Jack's comments and sorry for my mistake in nb first. Next I will try and report it later. So waiting for me. Thanks again.
By the way, to Bill, all your guesses are absolutely right.
The following is the code, and it does not work. I do not know whether the code itself is ok. Thanks
"
rstart = 0.001;
mysol = NDSolve[{d''[r] + (2/r + x'[r]/2 + c'[r]/c[r]) d'[r] ==
0, -(x'[r]/r) + c'[r]/c[r] (g'[r]/g[r] - x'[r]) == (
q^2 (b[r])^2 (a[r])^2)/(r^2 (c[r])^2 g[r])...
About serval differential equations where A, B, D, g, \chi, c are functions of r
\begin{eqnarray}
&-\frac{{\chi}'}{r}+\frac{c'}{c}\left(\frac{g'}{g} -{\chi}'\right)=\frac{e^{\chi}(q A B)^2}{r^2 g^2 c^2}& \\
&c c''+c c'\left(\frac{g'}{g}+\frac{2}{r} -\frac{{\chi}'}{2} \right)=-\frac{B'^2}{2...