\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( \left ( \alpha +\beta +1 \right ) \left ( x-a \right ) ^{2} \left ( x-b \right ) + \left ( 1-\alpha -\beta \right ) \left ( x-b \right ) ^{2} \left ( x-a \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( x-a \right ) ^{2} \left ( x-b \right ) ^{2}}}-{\frac {\alpha \,\beta \, \left ( a-b \right ) ^{2}y \left ( x \right ) }{ \left ( x-a \right ) ^{2} \left ( x-b \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.138018 (sec), leaf count = 50 \[ \left \{\left \{y(x)\to c_1 e^{\alpha (\log (x-a)-\log (x-b))}+c_2 e^{\beta (\log (x-a)-\log (x-b))}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {\frac {a-x}{b-x}} \right ) ^{\beta }+{\it \_C2}\, \left ( {\frac {a-x}{b-x}} \right ) ^{ \alpha } \right \} \]