\[ \boxed { {x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( x+\nu \right ) x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +\nu \, \left ( 2\,x+1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -\nu \, \left ( 1+x \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 47.362014 (sec), leaf count = 71 \[ \left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f818}^{(3)}(\unicode {f817}) \unicode {f817}^2-(\unicode {f817}+v) \unicode {f818}''(\unicode {f817}) \unicode {f817}-(\unicode {f817}+1) \nu \unicode {f818}(\unicode {f817})+(2 \unicode {f817} \nu +\nu ) \unicode {f818}'(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right )(x)\right \}\right \} \]
Maple: cpu = 0.172 (sec), leaf count = 55 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{x}}+{\it \_C2}\,{x} ^{{\frac {\nu }{2}}+{\frac {1}{2}}}{{\sl J}_{-\nu -1}\left (2\,\sqrt {\nu }\sqrt {x}\right )}+{\it \_C3}\,{x}^{{\frac {\nu }{2}}+{\frac {1}{2}}}{ {\sl Y}_{-\nu -1}\left (2\,\sqrt {\nu }\sqrt {x}\right )} \right \} \]