\[ y''(x)=-\frac {y(x) (a b x-\alpha \beta )}{(x-1) x^2}-\frac {y'(x) (x (a+b+1)+\alpha +\beta -1)}{(x-1) x} \] ✓ Mathematica : cpu = 0.179876 (sec), leaf count = 52
DSolve[Derivative[2][y][x] == -(((-(alpha*beta) + a*b*x)*y[x])/((-1 + x)*x^2)) - ((-1 + alpha + beta + (1 + a + b)*x)*Derivative[1][y][x])/((-1 + x)*x),y[x],x]
\[\left \{\left \{y(x)\to (-1)^{\alpha } c_1 x^{\alpha } \, _2F_1(a+\alpha ,\alpha +b;\alpha -\beta +1;x)+(-1)^{\beta } c_2 x^{\beta } \, _2F_1(a+\beta ,b+\beta ;-\alpha +\beta +1;x)\right \}\right \}\] ✓ Maple : cpu = 0.107 (sec), leaf count = 86
dsolve(diff(diff(y(x),x),x) = -((a+b+1)*x+alpha+beta-1)/x/(x-1)*diff(y(x),x)-(a*b*x-alpha*beta)/x^2/(x-1)*y(x),y(x))
\[y \left (x \right ) = \left (x -1\right )^{1-a -\alpha -b -\beta } \left (x^{\alpha } \hypergeom \left (\left [1-b -\beta , 1-a -\beta \right ], \left [1-\beta +\alpha \right ], x\right ) c_{1}+x^{\beta } \hypergeom \left (\left [1-\alpha -b , 1-a -\alpha \right ], \left [1+\beta -\alpha \right ], x\right ) c_{2}\right )\]