\[ \boxed { 2\,x \left ( x-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( \left ( 2\,v+5 \right ) x-2\,v-3 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( v+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.084511 (sec), leaf count = 60 \[ \left \{\left \{y(x)\to c_1 \, _2F_1\left (\frac {1}{2},v+1;v+\frac {3}{2};x\right )+c_2 i^{-2 v-1} x^{\frac {1}{2} (-2 v-1)} \, _2F_1\left (\frac {1}{2},-v;\frac {1}{2}-v;x\right )\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}({\frac {1}{2}},v+1;\,{\frac {3}{2}}+v;\,x)}+{\it \_C2}\,{x}^{-{\frac {1}{2}}-v} {\mbox {$_2$F$_1$}({\frac {1}{2}},-v;\,{\frac {1}{2}}-v;\,x)} \right \} \]