\[ -\frac {1}{16} b^4 x^{2/v} y(x)+(\nu -1) \nu ^2 (2 \nu -1) x^2 y''(x)+\nu ^4 x^4 y^{(4)}(x)+\nu ^3 (4 \nu -2) x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0588864 (sec), leaf count = 390
\[\left \{\left \{y(x)\to c_2 \left (\frac {i}{16}\right )^v v^{2 v} b^{2 v} \nu ^{-2 v} \left (x^{2/v}\right )^{v/2} \, _0F_3\left (;\frac {v}{2}+1,1-\frac {v}{2 \nu },-\frac {v}{2 \nu }+\frac {v}{2}+1;\frac {b^4 v^4 x^{2/v}}{256 \nu ^4}\right )+c_3 \left (\frac {i}{16}\right )^{\frac {v}{\nu }} v^{\frac {2 v}{\nu }} \nu ^{-\frac {2 v}{\nu }} b^{\frac {2 v}{\nu }} \left (x^{2/v}\right )^{\frac {v}{2 \nu }} \, _0F_3\left (;1-\frac {v}{2},\frac {v}{2 \nu }+1,\frac {v}{2 \nu }-\frac {v}{2}+1;\frac {b^4 v^4 x^{2/v}}{256 \nu ^4}\right )+c_4 \left (\frac {i}{16}\right )^{\frac {(\nu +1) v}{\nu }} v^{\frac {2 (\nu +1) v}{\nu }} \nu ^{-\frac {2 (\nu +1) v}{\nu }} b^{\frac {2 (\nu +1) v}{\nu }} \left (x^{2/v}\right )^{\frac {(\nu +1) v}{2 \nu }} \, _0F_3\left (;\frac {v}{2}+1,\frac {v}{2 \nu }+1,\frac {v}{2 \nu }+\frac {v}{2}+1;\frac {b^4 v^4 x^{2/v}}{256 \nu ^4}\right )+c_1 \, _0F_3\left (;1-\frac {v}{2},1-\frac {v}{2 \nu },-\frac {v}{2 \nu }-\frac {v}{2}+1;\frac {b^4 v^4 x^{2/v}}{256 \nu ^4}\right )\right \}\right \}\] ✓ Maple : cpu = 2.208 (sec), leaf count = 143
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {{\sl J}_{ \left ( \left \lfloor {\nu }^{-1}\right \rfloor \right ) ^{-1}}\left ({\frac {1}{\left \lfloor {\nu }^{-1}\right \rfloor }\sqrt {{\frac {{b}^{2}}{{\nu }^{2}}}}{x}^{{\frac {\left \lfloor {\nu }^{-1}\right \rfloor }{2}}}}\right )}{\it \_C1}+{{\sl Y}_{ \left ( \left \lfloor {\nu }^{-1}\right \rfloor \right ) ^{-1}}\left ({\frac {1}{\left \lfloor {\nu }^{-1}\right \rfloor }\sqrt {{\frac {{b}^{2}}{{\nu }^{2}}}}{x}^{{\frac {\left \lfloor {\nu }^{-1}\right \rfloor }{2}}}}\right )}{\it \_C2}+{{\sl J}_{ \left ( \left \lfloor {\nu }^{-1}\right \rfloor \right ) ^{-1}}\left ({\frac {1}{\left \lfloor {\nu }^{-1}\right \rfloor }\sqrt {-{\frac {{b}^{2}}{{\nu }^{2}}}}{x}^{{\frac {\left \lfloor {\nu }^{-1}\right \rfloor }{2}}}}\right )}{\it \_C3}+{{\sl Y}_{ \left ( \left \lfloor {\nu }^{-1}\right \rfloor \right ) ^{-1}}\left ({\frac {1}{\left \lfloor {\nu }^{-1}\right \rfloor }\sqrt {-{\frac {{b}^{2}}{{\nu }^{2}}}}{x}^{{\frac {\left \lfloor {\nu }^{-1}\right \rfloor }{2}}}}\right )}{\it \_C4} \right ) \right \} \]