\[ y'(x) (x (\text {a1}+\text {b1}+1)-\text {d1})+\text {a1} \text {b1} \text {d1}+(x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.222542 (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 = 1.168 (sec), leaf count = 77
\[ \left \{ y \left ( x \right ) =\int \!- \left ( x-1 \right ) ^{-{\it a1}-{\it b1}-1+{\it d1}} \left ( {\it a1}\,{\it b1}\, \left ( {\it signum} \left ( x-1 \right ) \right ) ^{{\it a1}+{\it b1}-{\it d1}} \left ( -{\it signum} \left ( x-1 \right ) \right ) ^{-{\it a1}-{\it b1}+{\it d1}}{\mbox {$_2$F$_1$}({\it d1},-{\it a1}-{\it b1}+{\it d1};\,1+{\it d1};\,x)}-{x}^{-{\it d1}}{\it \_C1} \right ) \,{\rm d}x+{\it \_C2} \right \} \]