\[ \boxed { x{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( x+2\,v \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( x-2\,v-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( x-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.210027 (sec), leaf count = 93 \[ \left \{\left \{y(x)\to \frac {c_3 e^x x^{2 v+2} \Gamma \left (v+\frac {3}{2}\right ) \, _1\tilde {F}_1\left (v+\frac {3}{2};2 v+3;-2 x\right )}{\Gamma \left (\frac {1}{2}-v\right )}+c_2 2^{-2 v-2} e^x G_{2,3}^{2,1}\left (2 x\left | \begin {array}{c} 1,v+\frac {3}{2} \\ 1,2 (v+1),0 \\ \end {array} \right .\right )+c_1 e^x\right \}\right \} \]
Maple: cpu = 0.219 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{x}}+{\it \_C2}\,{x} ^{v+1}{{\sl I}_{-v-1}\left (x\right )}+{\it \_C3}\,{x}^{v+1}{{\sl K}_{v+ 1}\left (x\right )} \right \} \]