\[
\boxed{
2\,x \left( x-1 \right) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) + \left(  \left( 2\,v+5 \right) x-2\,v-3 \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) + \left( v+1 \right) y \left( x \right) =0}
\]