\[ -\frac {1}{16} b^4 y(x)+x (2 n-2 \nu +4) y^{(3)}(x)+(n-\nu +1) (n-\nu +2) y''(x)+x^2 y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.171222 (sec), leaf count = 319
\[\left \{\left \{y(x)\to c_4 i^{-n+\nu +1} 2^{3 n-3 \nu -3} b^{2 (-n+\nu +1)+n-\nu -2} x^{\frac {1}{2} (n-\nu -2)-n+\nu +1} \Gamma (-n+\nu +2) \left (I_{\nu -n}\left (b \sqrt {x}\right )-J_{\nu -n}\left (b \sqrt {x}\right )\right )+c_3 i^{\nu -n} 2^{3 n-3 \nu -1} b^{2 (\nu -n)+n-\nu } x^{\frac {n-\nu }{2}-n+\nu } \Gamma (-n+\nu +1) \left (J_{\nu -n}\left (b \sqrt {x}\right )+I_{\nu -n}\left (b \sqrt {x}\right )\right )+i c_2 2^{n-\nu -3} b^{\nu -n} x^{\frac {1}{2} (-n+\nu -2)+1} \Gamma (n-\nu +2) \left (I_{n-\nu }\left (b \sqrt {x}\right )-J_{n-\nu }\left (b \sqrt {x}\right )\right )+c_1 2^{n-\nu -1} b^{\nu -n} x^{\frac {\nu -n}{2}} \Gamma (n-\nu +1) \left (J_{n-\nu }\left (b \sqrt {x}\right )+I_{n-\nu }\left (b \sqrt {x}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.193 (sec), leaf count = 93
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {n}{2}}+{\frac {\nu }{2}}}{{\sl I}_{n-\nu }\left (b\sqrt {x}\right )}+{\it \_C2}\,{x}^{-{\frac {n}{2}}+{\frac {\nu }{2}}}{{\sl J}_{n-\nu }\left (b\sqrt {x}\right )}+{\it \_C3}\,{x}^{-{\frac {n}{2}}+{\frac {\nu }{2}}}{{\sl K}_{n-\nu }\left (b\sqrt {x}\right )}+{\it \_C4}\,{x}^{-{\frac {n}{2}}+{\frac {\nu }{2}}}{{\sl Y}_{n-\nu }\left (b\sqrt {x}\right )} \right \} \]