\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( \left ( \alpha +\beta +1 \right ) {x}^{2}- \left ( \alpha +\beta +1+a \left ( \gamma 1+\delta \right ) -\delta \right ) x+a\gamma 1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( x-1 \right ) \left ( x-a \right ) }}-{\frac { \left ( \alpha \,\beta \,x-q \right ) y \left ( x \right ) }{x \left ( x-1 \right ) \left ( x-a \right ) }}=0} \]
Mathematica: cpu = 6.409814 (sec), leaf count = 99 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\unicode {f817} \alpha \beta -q) \unicode {f818}(\unicode {f817})+\left (\alpha \unicode {f817}^2+\beta \unicode {f817}^2+\unicode {f817}^2-\alpha \unicode {f817}-\beta \unicode {f817}-a \delta \unicode {f817}+\delta \unicode {f817}-a \text {gamma1} \unicode {f817}-\unicode {f817}+a \text {gamma1}\right ) \unicode {f818}'(\unicode {f817})-(\unicode {f817}-1) \unicode {f817} (a-\unicode {f817}) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 64 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunG} \left ( a,q,\alpha ,\beta ,\gamma 1,\delta ,x \right ) +{\it \_C2}\,{x}^{1-\gamma 1}{\it HeunG } \left ( a,q- \left ( -1+\gamma 1 \right ) \left ( \delta \, \left ( a-1 \right ) +\alpha +\beta -\gamma 1+1 \right ) ,\beta +1-\gamma 1,\alpha +1- \gamma 1,-\gamma 1+2,\delta ,x \right ) \right \} \]