# DSolve function is not working for Hypergeometric Function

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]

• 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. – aooiiii Jan 17 at 3:25
• Maple 2019.2.1 also can't solve. – Mariusz Iwaniuk Jan 18 at 10:48