\[ \boxed { x \left ( x-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( \left ( {\it a1}+{\it b1}+1 \right ) x-{\it d1} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{\it a1}\,{\it b1}\,{\it d1}=0} \]
Mathematica: cpu = 0.160020 (sec), leaf count = 65 \[ \left \{\left \{y(x)\to \text {a1} \text {b1} x \Gamma (\text {d1}+1) \, _3\tilde {F}_2(1,\text {a1}+\text {b1}+1,1;\text {d1}+1,2;x)-\frac {c_1 x^{1-\text {d1}} \, _2F_1(1-\text {d1},\text {a1}+\text {b1}-\text {d1}+1;2-\text {d1};x)}{\text {d1}-1}+c_2\right \}\right \} \]
Maple: cpu = 0.296 (sec), leaf count = 76 \[ \left \{ y \left ( x \right ) =\int \! \left ( - \left ( {\it signum} \left ( x-1 \right ) \right ) ^{{\it a1}+{\it b1}-{\it d1}} \left ( -{ \it signum} \left ( x-1 \right ) \right ) ^{-{\it a1}-{\it b1}+{\it d1}} {\mbox {$_2$F$_1$}({\it d1},-{\it a1}-{\it b1}+{\it d1};\,1+{\it d1};\,x)} {\it a1}\,{\it b1}+{x}^{-{\it d1}}{\it \_C1} \right ) \left ( x-1 \right ) ^{-{\it a1}-{\it b1}-1+{\it d1}}\,{\rm d}x+{\it \_C2} \right \} \]