\[ y''(x)=-\frac {y(x) \left (-4 n^2 x-v (v+1) (x-1)^2\right )}{4 (x-1)^2 x^2}-\frac {(3 x-1) y'(x)}{2 (x-1) x} \] ✓ Mathematica : cpu = 0.293093 (sec), leaf count = 217
\[\left \{\left \{y(x)\to c_2 (-1)^{\frac {1}{2} (-2 v-3)+1} x^{\frac {1}{4} (-2 v-3)+1} e^{\frac {1}{4} (-2 \log (1-x)-\log (x))} (x-1)^{\frac {1}{2} \left (n+\frac {1}{2} (2 n+1)+\frac {1}{2} (-2 v-3)+v+2\right )} \, _2F_1\left (\frac {1}{2} (2 n+1)+\frac {1}{2} (-2 v-3)+1,n+\frac {1}{2} (-2 v-3)+v+2;\frac {1}{2} (-2 v-3)+2;x\right )+c_1 x^{\frac {1}{4} (2 v+3)} e^{\frac {1}{4} (-2 \log (1-x)-\log (x))} (x-1)^{\frac {1}{2} \left (n+\frac {1}{2} (2 n+1)+\frac {1}{2} (-2 v-3)+v+2\right )} \, _2F_1\left (\frac {1}{2} (2 n+1),n+v+1;\frac {1}{2} (2 v+3);x\right )\right \}\right \}\] ✓ Maple : cpu = 0.425 (sec), leaf count = 68
\[ \left \{ y \left ( x \right ) = \left ( x-1 \right ) ^{-n} \left ( {x}^{-{\frac {v}{2}}}{\mbox {$_2$F$_1$}(-v-n,-n+{\frac {1}{2}};\,{\frac {1}{2}}-v;\,x)}{\it \_C1}+{x}^{{\frac {1}{2}}+{\frac {v}{2}}}{\mbox {$_2$F$_1$}(v-n+1,-n+{\frac {1}{2}};\,{\frac {3}{2}}+v;\,x)}{\it \_C2} \right ) \right \} \]