\[ ((2 v+5) x-2 v-3) y'(x)+(v+1) y(x)+2 (x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.097837 (sec), leaf count = 59
\[\left \{\left \{y(x)\to c_1 \, _2F_1\left (\frac {1}{2},v+1;v+\frac {3}{2};x\right )-i c_2 i^{-2 v} x^{-v-\frac {1}{2}} \, _2F_1\left (\frac {1}{2},-v;\frac {1}{2}-v;x\right )\right \}\right \}\]
✓ Maple : cpu = 0.096 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}({\frac {1}{2}},v+1;\,{\frac {3}{2}}+v;\,x)}+{\it \_C2}\,{x}^{-{\frac {1}{2}}-v}{\mbox {$_2$F$_1$}({\frac {1}{2}},-v;\,{\frac {1}{2}}-v;\,x)} \right \} \]