\[ y''(x)=-\frac {y'(x) \left (-x (a (\delta +\text {gamma1})+\alpha +\beta -\delta +1)+a \text {gamma1}+x^2 (\alpha +\beta +1)\right )}{(x-1) x (x-a)}-\frac {y(x) (\alpha \beta x-q)}{(x-1) x (x-a)} \] ✗ Mathematica : cpu = 6.3241 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{(\unicode {f817} \alpha \beta -q) \unicode {f818}(\unicode {f817})+\left (\alpha \unicode {f817}^2+\beta \unicode {f817}^2+\unicode {f817}^2-\alpha \unicode {f817}-\beta \unicode {f817}-a \delta \unicode {f817}+\delta \unicode {f817}-a \text {gamma1} \unicode {f817}-\unicode {f817}+a \text {gamma1}\right ) \unicode {f818}'(\unicode {f817})-(\unicode {f817}-1) \unicode {f817} (a-\unicode {f817}) \unicode {f818}''(\unicode {f817})=0,\unicode {f818}(2)=c_1,\unicode {f818}'(2)=c_2\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.777 (sec), leaf count = 64
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunG} \left ( a,q,\alpha ,\beta ,\gamma 1,\delta ,x \right ) +{\it \_C2}\,{x}^{1-\gamma 1}{\it HeunG} \left ( a,q- \left ( -1+\gamma 1 \right ) \left ( \delta \, \left ( a-1 \right ) +\alpha +\beta -\gamma 1+1 \right ) ,\beta +1-\gamma 1,\alpha +1-\gamma 1,-\gamma 1+2,\delta ,x \right ) \right \} \]