\[ -\frac {1}{16} b^4 x^{2/v} y(x)+\nu ^4 x^4 y^{(4)}(x)+\nu ^3 (4 \nu -2) x^3 y^{(3)}(x)+(\nu -1) \nu ^2 (2 \nu -1) x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0622124 (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 = 0.234 (sec), leaf count = 143
\[y \relax (x ) = \sqrt {x}\, \left (\BesselJ \left (\frac {1}{{\lfloor \frac {1}{\nu }\rfloor }}, \frac {\sqrt {\frac {b^{2}}{\nu ^{2}}}\, x^{\frac {{\lfloor \frac {1}{\nu }\rfloor }}{2}}}{{\lfloor \frac {1}{\nu }\rfloor }}\right ) c_{1}+\BesselY \left (\frac {1}{{\lfloor \frac {1}{\nu }\rfloor }}, \frac {\sqrt {\frac {b^{2}}{\nu ^{2}}}\, x^{\frac {{\lfloor \frac {1}{\nu }\rfloor }}{2}}}{{\lfloor \frac {1}{\nu }\rfloor }}\right ) c_{2}+\BesselJ \left (\frac {1}{{\lfloor \frac {1}{\nu }\rfloor }}, \frac {\sqrt {-\frac {b^{2}}{\nu ^{2}}}\, x^{\frac {{\lfloor \frac {1}{\nu }\rfloor }}{2}}}{{\lfloor \frac {1}{\nu }\rfloor }}\right ) c_{3}+\BesselY \left (\frac {1}{{\lfloor \frac {1}{\nu }\rfloor }}, \frac {\sqrt {-\frac {b^{2}}{\nu ^{2}}}\, x^{\frac {{\lfloor \frac {1}{\nu }\rfloor }}{2}}}{{\lfloor \frac {1}{\nu }\rfloor }}\right ) c_{4}\right )\]