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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, enter image description here

I would appreciate it if you can help me. Thank you again for your help!

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. I would appreciate it if you can help me. Thank you again for your help!

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, enter image description here

I would appreciate it if you can help me. Thank you again for your help!

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The problem of solutions of partialordinary differential equations

I am using MMA to compute the solution of a system of partialordinary 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. I would appreciate it if you can help me. Thank you again for your help!

The problem of solutions of partial differential equations

I am using MMA to compute the solution of a system of partial 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. I would appreciate it if you can help me. Thank you again for your help!

The problem of solutions of ordinary differential equations

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. I would appreciate it if you can help me. Thank you again for your help!

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The problem of solutions of partial differential equations

I am using MMA to compute the solution of a system of partial 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. I would appreciate it if you can help me. Thank you again for your help!