\[ y''(x)=-\frac {y(x) (a b x-\alpha \beta )}{(x-1) x^2}-\frac {y'(x) (x (a+b+1)+\alpha +\beta -1)}{(x-1) x} \] ✓ Mathematica : cpu = 0.211231 (sec), leaf count = 52
\[\left \{\left \{y(x)\to (-1)^{\alpha } c_1 x^{\alpha } \, _2F_1(a+\alpha ,\alpha +b;\alpha -\beta +1;x)+(-1)^{\beta } c_2 x^{\beta } \, _2F_1(a+\beta ,b+\beta ;-\alpha +\beta +1;x)\right \}\right \}\] ✓ Maple : cpu = 0.139 (sec), leaf count = 86
\[\{y \left (x \right ) = \left (c_{1} x^{\alpha } \hypergeom \left (\left [-b -\beta +1, -a -\beta +1\right ], \left [\alpha -\beta +1\right ], x\right )+c_{2} x^{\beta } \hypergeom \left (\left [-a -\alpha +1, -\alpha -b +1\right ], \left [-\alpha +\beta +1\right ], x\right )\right ) \left (x -1\right )^{-a -\alpha -b -\beta +1}\}\]