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