\[ y''(x)=-\frac {y'(x) \left (a (b+2) x^2+x (c-d+1)\right )}{x^2 (a x+1)}-\frac {y(x) (a b x-c d)}{x^2 (a x+1)} \] ✓ Mathematica : cpu = 0.180147 (sec), leaf count = 66
\[\left \{\left \{y(x)\to c_1 a^{-c} x^{-c} \, _2F_1(1-c,b-c;-c-d+1;-a x)+c_2 a^d x^d \, _2F_1(d+1,b+d;c+d+1;-a x)\right \}\right \}\] ✓ Maple : cpu = 0.111 (sec), leaf count = 76
\[y \relax (x ) = \left (a x +1\right )^{-b +c -d} \left (\hypergeom \left (\left [c , 1-b +c \right ], \left [1+d +c \right ], -a x \right ) x^{d} c_{1}+\hypergeom \left (\left [-d , 1-b -d \right ], \left [1-d -c \right ], -a x \right ) x^{-c} c_{2}\right )\]