How exactly did you derive this equation for ##B##?
From the first equation, you have that: ##B=\frac{1}{\epsilon+1}(A'-\frac{m}{r}A)##. When you substitute this expression into the second equation, you get:
## -(A''+\frac{m}{r^2}A-\frac{m}{r}A')...
I have the following system of differential equations, for the functions ##A(r)## and ##B(r)##:
##A'-\frac{m}{r}A=(\epsilon+1)B##
and
##-B' -\frac{m+1}{r}B=(\epsilon-1)A##
##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a...