\[ y''(x)=-\frac {y(x) \left (-4 n^2 x-v (v+1) (x-1)^2\right )}{4 (x-1)^2 x^2}-\frac {(3 x-1) y'(x)}{2 (x-1) x} \] ✓ Mathematica : cpu = 0.406542 (sec), leaf count = 91
\[\left \{\left \{y(x)\to \frac {(-1)^{-v} (x-1)^{n+\frac {1}{2}} x^{-v/2} \left (c_1 (-1)^v x^{v+\frac {1}{2}} \, _2F_1\left (n+\frac {1}{2},n+v+1;v+\frac {3}{2};x\right )-i c_2 \, _2F_1\left (n+\frac {1}{2},n-v;\frac {1}{2}-v;x\right )\right )}{\sqrt {1-x}}\right \}\right \}\]
✓ Maple : cpu = 0.151 (sec), leaf count = 68
\[ \left \{ y \left ( x \right ) = \left ( x-1 \right ) ^{-n} \left ( {x}^{-{\frac {v}{2}}}{\mbox {$_2$F$_1$}(-v-n,-n+{\frac {1}{2}};\,{\frac {1}{2}}-v;\,x)}{\it \_C1}+{x}^{{\frac {1}{2}}+{\frac {v}{2}}}{\mbox {$_2$F$_1$}(v-n+1,-n+{\frac {1}{2}};\,{\frac {3}{2}}+v;\,x)}{\it \_C2} \right ) \right \} \]