\[ -\frac {1}{16} b^4 y(x)+x (2 n-2 \nu +4) y^{(3)}(x)+(n-\nu +1) (n-\nu +2) y''(x)+x^2 y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.174233 (sec), leaf count = 222
\[\left \{\left \{y(x)\to i^{-n} 2^{n-3 \nu -3} b^{\nu -n} x^{\frac {\nu -n}{2}} \left (i^n 4^{\nu } \left (4 c_1 \Gamma (n-\nu +1)-i c_2 \Gamma (n-\nu +2)\right ) J_{n-\nu }\left (b \sqrt {x}\right )+i^n 4^{\nu } \left (4 c_1 \Gamma (n-\nu +1)+i c_2 \Gamma (n-\nu +2)\right ) I_{n-\nu }\left (b \sqrt {x}\right )+4^n i^{\nu } \left (\left (4 c_3 \Gamma (-n+\nu +1)-i c_4 \Gamma (-n+\nu +2)\right ) J_{\nu -n}\left (b \sqrt {x}\right )+\left (4 c_3 \Gamma (-n+\nu +1)+i c_4 \Gamma (-n+\nu +2)\right ) I_{\nu -n}\left (b \sqrt {x}\right )\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.2 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {n}{2}}+{\frac {\nu }{2}}} \left ( {{\sl K}_{n-\nu }\left (b\sqrt {x}\right )}{\it \_C3}+{{\sl I}_{n-\nu }\left (b\sqrt {x}\right )}{\it \_C1}+{{\sl Y}_{n-\nu }\left (b\sqrt {x}\right )}{\it \_C4}+{{\sl J}_{n-\nu }\left (b\sqrt {x}\right )}{\it \_C2} \right ) \right \} \]