\[ \nu (2 x+1) y'(x)-\nu (x+1) y(x)-x (v+x) y''(x)+x^2 y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 30.3474 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f818}^{(3)}(\unicode {f817}) \unicode {f817}^2-(\unicode {f817}+v) \unicode {f818}''(\unicode {f817}) \unicode {f817}-(\unicode {f817}+1) \nu \unicode {f818}(\unicode {f817})+(2 \unicode {f817} \nu +\nu ) \unicode {f818}'(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right )(x)\right \}\right \}\]
✓ Maple : cpu = 0.195 (sec), leaf count = 55
\[ \left \{ y \left ( x \right ) ={{\rm e}^{x}}{\it \_C1}+{\it \_C2}\,{x}^{{\frac {\nu }{2}}+{\frac {1}{2}}}{{\sl J}_{-\nu -1}\left (2\,\sqrt {\nu }\sqrt {x}\right )}+{\it \_C3}\,{x}^{{\frac {\nu }{2}}+{\frac {1}{2}}}{{\sl Y}_{-\nu -1}\left (2\,\sqrt {\nu }\sqrt {x}\right )} \right \} \]