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I am trying to get the solution of second order differential equation, but it is not working. Any idea about it will help me a lot.

    DSolve[{(54 g[r] + 
    3 r (13 Derivative[1][f][r] + 5 Derivative[1][g][r] + 
       4 r (f^\[Prime]\[Prime])[r]))/
   r^2 == (59 g[r])/r + (
    40 (66 - 89 r + 28 r^2) Hypergeometric2F1[2 - Sqrt[3], 
      2 + Sqrt[3], 4, (9 r)/10])/(
    40 Hypergeometric2F1[2 - Sqrt[3], 2 + Sqrt[3], 4, 9/10] + 
     3 Hypergeometric2F1[3 - Sqrt[3], 3 + Sqrt[3], 5, 9/10]) + 
    46 Derivative[1][f][r] + 13 Derivative[1][g][r] + 
    11 r (f^\[Prime]\[Prime])[r], (1/(
   r^4))(132 g[r] - 
     125 r g[r] + (r^3 (-33 + 
          28 r) (40 Hypergeometric2F1[2 - Sqrt[3], 2 + Sqrt[3], 4, (
            9 r)/10] + 
          9 (-2 + r) Hypergeometric2F1[3 - Sqrt[3], 3 + Sqrt[3], 5, (
            9 r)/10]))/(40 Hypergeometric2F1[2 - Sqrt[3], 2 + Sqrt[3],
           4, 9/10] + 
        3 Hypergeometric2F1[3 - Sqrt[3], 3 + Sqrt[3], 5, 9/10]) + 
     15 r Derivative[1][f][r] - 39 r Derivative[1][g][r] + 
     59 r^2 Derivative[1][g][r] - 15 r^2 (f^\[Prime]\[Prime])[r] + 
     13 r^3 (f^\[Prime]\[Prime])[r] - 
     27 r^2 (g^\[Prime]\[Prime])[r] + 
     24 r^3 (g^\[Prime]\[Prime])[r]) == 0}, {f[r], g[r]}, r]
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  • 1
    $\begingroup$ Although this is correct, instead of Derivative[1][f][r] you can simply write f'[r], where ' is a plain ASCII single quote, not the special \[Prime] symbol. Speaking of which, Mathematica won't understand that (f^\[Prime]\[Prime])[r] is the second derivative. Write it as f''[r] (or Derivative[2][f][r] if you wish). Unfortunately though, writing the equations correctly didn't help Mathematica solve them. But it's unrealistic to expect automatically obtaining closed-form solutions of such complex equations, even if you happen to know they exist. $\endgroup$ – aooiiii Jan 17 at 3:25
  • $\begingroup$ Maple 2019.2.1 also can't solve. $\endgroup$ – Mariusz Iwaniuk Jan 18 at 10:48

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