\[ y''(x)=-\frac {y(x) \left (v (v+1) (x-1)-a^2 x\right )}{4 (x-1)^2 x^2}-\frac {(3 x-1) y'(x)}{2 (x-1) x} \] ✓ Mathematica : cpu = 0.239251 (sec), leaf count = 235
\[\left \{\left \{y(x)\to c_2 (-1)^{\frac {1}{2} (-2 v-3)+1} x^{\frac {1}{4} (-2 v-3)+1} e^{\frac {1}{4} (-2 \log (1-x)-\log (x))} (x-1)^{\frac {1}{2} \left (\frac {1}{2} (a+v+1)+\frac {1}{2} (a+v+2)+\frac {1}{2} (-2 v-3)+1\right )} \, _2F_1\left (\frac {1}{2} (-2 v-3)+\frac {1}{2} (a+v+1)+1,\frac {1}{2} (-2 v-3)+\frac {1}{2} (a+v+2)+1;\frac {1}{2} (-2 v-3)+2;x\right )+c_1 x^{\frac {1}{4} (2 v+3)} e^{\frac {1}{4} (-2 \log (1-x)-\log (x))} (x-1)^{\frac {1}{2} \left (\frac {1}{2} (a+v+1)+\frac {1}{2} (a+v+2)+\frac {1}{2} (-2 v-3)+1\right )} \, _2F_1\left (\frac {1}{2} (a+v+1),\frac {1}{2} (a+v+2);\frac {1}{2} (2 v+3);x\right )\right \}\right \}\] ✓ Maple : cpu = 0.418 (sec), leaf count = 76
\[ \left \{ y \left ( x \right ) = \left ( x-1 \right ) ^{-{\frac {a}{2}}} \left ( {x}^{-{\frac {v}{2}}}{\mbox {$_2$F$_1$}(-{\frac {v}{2}}-{\frac {a}{2}},{\frac {1}{2}}-{\frac {v}{2}}-{\frac {a}{2}};\,{\frac {1}{2}}-v;\,x)}{\it \_C1}+{x}^{{\frac {1}{2}}+{\frac {v}{2}}}{\mbox {$_2$F$_1$}(1+{\frac {v}{2}}-{\frac {a}{2}},{\frac {1}{2}}+{\frac {v}{2}}-{\frac {a}{2}};\,{\frac {3}{2}}+v;\,x)}{\it \_C2} \right ) \right \} \]