\[ \boxed { {\nu }^{4}{x}^{4}{\it d4y} \left ( x \right ) + \left ( 4\,\nu -2 \right ) {\nu }^{3}{x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( \nu -1 \right ) \left ( 2\,\nu -1 \right ) {\nu }^{2}{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -1/16\,{b}^{4}{x}^{2\,{\nu }^{-1}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.094012 (sec), leaf count = 390 \[ \left \{\left \{y(x)\to c_1 \, _0F_3\left (;1-\frac {v}{2},1-\frac {v}{2 \nu },-\frac {v}{2 \nu }-\frac {v}{2}+1;\frac {b^4 v^4 x^{2/v}}{256 \nu ^4}\right )+c_2 \left (\frac {i}{16}\right )^v v^{2 v} b^{2 v} \nu ^{-2 v} \left (x^{2/v}\right )^{v/2} \, _0F_3\left (;\frac {v}{2}+1,1-\frac {v}{2 \nu },-\frac {v}{2 \nu }+\frac {v}{2}+1;\frac {b^4 v^4 x^{2/v}}{256 \nu ^4}\right )+c_3 \left (\frac {i}{16}\right )^{\frac {v}{\nu }} v^{\frac {2 v}{\nu }} \nu ^{-\frac {2 v}{\nu }} b^{\frac {2 v}{\nu }} \left (x^{2/v}\right )^{\frac {v}{2 \nu }} \, _0F_3\left (;1-\frac {v}{2},\frac {v}{2 \nu }+1,\frac {v}{2 \nu }-\frac {v}{2}+1;\frac {b^4 v^4 x^{2/v}}{256 \nu ^4}\right )+c_4 \left (\frac {i}{16}\right )^{\frac {(\nu +1) v}{\nu }} v^{\frac {2 (\nu +1) v}{\nu }} \nu ^{-\frac {2 (\nu +1) v}{\nu }} b^{\frac {2 (\nu +1) v}{\nu }} \left (x^{2/v}\right )^{\frac {(\nu +1) v}{2 \nu }} \, _0F_3\left (;\frac {v}{2}+1,\frac {v}{2 \nu }+1,\frac {v}{2 \nu }+\frac {v}{2}+1;\frac {b^4 v^4 x^{2/v}}{256 \nu ^4}\right )\right \}\right \} \]
Maple: cpu = 0.093 (sec), leaf count = 151 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}{{\sl J}_{ \left ( \left \lfloor {\nu }^{-1}\right \rfloor \right ) ^{-1}}\left ({\frac {1}{ \left \lfloor {\nu }^{-1}\right \rfloor }\sqrt {{\frac {{b}^{2}}{{\nu }^{2} }}}{x}^{{\frac {\left \lfloor {\nu }^{-1}\right \rfloor }{2}}}}\right )}+{ \it \_C2}\,\sqrt {x}{{\sl Y}_{ \left ( \left \lfloor {\nu }^{-1} \right \rfloor \right ) ^{-1}}\left ({\frac {1}{\left \lfloor {\nu }^{-1} \right \rfloor }\sqrt {{\frac {{b}^{2}}{{\nu }^{2}}}}{x}^{{\frac { \left \lfloor {\nu }^{-1}\right \rfloor }{2}}}}\right )}+{\it \_C3}\,\sqrt {x}{{\sl J}_{ \left ( \left \lfloor {\nu }^{-1}\right \rfloor \right ) ^{-1 }}\left ({\frac {1}{\left \lfloor {\nu }^{-1}\right \rfloor }\sqrt {-{ \frac {{b}^{2}}{{\nu }^{2}}}}{x}^{{\frac {\left \lfloor {\nu }^{-1} \right \rfloor }{2}}}}\right )}+{\it \_C4}\,\sqrt {x}{{\sl Y}_{ \left ( \left \lfloor {\nu }^{-1}\right \rfloor \right ) ^{-1}}\left ({\frac {1}{ \left \lfloor {\nu }^{-1}\right \rfloor }\sqrt {-{\frac {{b}^{2}}{{\nu }^{2 }}}}{x}^{{\frac {\left \lfloor {\nu }^{-1}\right \rfloor }{2}}}}\right )} \right \} \]