\[ y'(x) (x (\text {a1}+\text {b1}+1)-\text {d1})+\text {a1} \text {b1} \text {d1}+(x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.246186 (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 = 0.712 (sec), leaf count = 77
\[\{y \left (x \right ) = c_{2}+\int -\left (\mathit {a1} \mathit {b1} \left (-\mathrm {signum}\left (x -1\right )\right )^{-\mathit {a1} -\mathit {b1} +\mathit {d1}} \mathrm {signum}\left (x -1\right )^{\mathit {a1} +\mathit {b1} -\mathit {d1}} \hypergeom \left (\left [\mathit {d1} , -\mathit {a1} -\mathit {b1} +\mathit {d1} \right ], \left [\mathit {d1} +1\right ], x\right )-c_{1} x^{-\mathit {d1}}\right ) \left (x -1\right )^{-\mathit {a1} -\mathit {b1} +\mathit {d1} -1}d x\}\]