\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( \left ( a+b+1 \right ) x+\alpha +\beta -1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( x-1 \right ) }}-{\frac { \left ( abx-\alpha \,\beta \right ) y \left ( x \right ) }{{x}^{2} \left ( x-1 \right ) }}=0} \]
Mathematica: cpu = 0.264534 (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 = 0.093 (sec), leaf count = 103 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{\alpha } \left ( x-1 \right ) ^{1-a-\alpha -b-\beta } {\mbox {$_2$F$_1$}(1-b-\beta ,1-a-\beta ;\,1+\alpha -\beta ;\,x)}+{\it \_C2 }\,{x}^{\beta } \left ( x-1 \right ) ^{1-a-\alpha -b-\beta } {\mbox {$_2$F$_1$}(1-a-\alpha ,1-\alpha -b;\,1-\alpha +\beta ;\,x)} \right \} \]