I am using MMA to compute the solution of a system of ordinary differential equations, they are as follows,
Clear["`*"]
DSolve[{(
g[r] + G1[r])*(1/r^2 +
1/r ( Derivative[1][g][r] + Derivative[1][G1][r])/(
g[r] + G1[r])) ==
g[r]*(1/r^2 + 1/r Derivative[1][g][r]/g[r]), (
g[r] + G1[r])*(1/r^2 +
1/r ( Derivative[1][f][r] + Derivative[1][F1][r])/(
f[r] + F1[r])) == g[r]*(1/r^2 + 1/r Derivative[1][f][r]/f[r]),
G1[1] == -1}, {G1[r], F1[r]}, r]
I want to obtain the solutions of them, but I don't quite understand our these results. And my try of solutions are as follow,
I would appreciate it if you can help me. Thank you again for your help!