\[ \boxed { {x}^{4}{\it d4y} \left ( x \right ) +4\,{x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( 4\,{n}^{2}+3 \right ) {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 12\,{n}^{2}-3 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( 4\,{x}^{4}+12\,{n}^{2}-3 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 1.386176 (sec), leaf count = 230 \[ \left \{\left \{y(x)\to \frac {\sqrt [4]{-1} c_1 x \, _0F_3\left (;\frac {1}{2},\frac {3}{2}-\frac {n}{2},\frac {n}{2}+\frac {3}{2};\frac {x^4}{64}\right )}{2 \sqrt {2}}+c_3 (-1)^{\frac {1}{4} (-2 n-1)} 2^{2 n+\frac {1}{2} (2 n+1)+1} x^{-2 n-1} \, _0F_3\left (;1-n,\frac {1}{2}-\frac {n}{2},-\frac {n}{2};\frac {x^4}{64}\right )+c_4 (-1)^{\frac {1}{4} (2 n-1)} 2^{\frac {1}{2} (1-2 n)-2 n+1} x^{2 n-1} \, _0F_3\left (;\frac {n}{2}+\frac {1}{2},\frac {n}{2},n+1;\frac {x^4}{64}\right )+\frac {(-1)^{3/4} c_2 x^3 \, _0F_3\left (;\frac {3}{2},2-\frac {n}{2},\frac {n}{2}+2;\frac {x^4}{64}\right )}{16 \sqrt {2}}\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 156 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( \left ( { {\rm ber}_{n}\left (x\right )} \right ) ^{2}+ \left ( {{\rm bei}_{n}\left ( x\right )} \right ) ^{2} \right ) }{x}}+{\it \_C2}\,{x}^{3} {\mbox {$_0$F$_3$}(\ ;\,{\frac {3}{2}},2-{\frac {n}{2}},2+{\frac {n}{2}};\,{\frac {{x}^{4}}{64}})} +{\it \_C3}\,x {\mbox {$_0$F$_3$}(\ ;\,{\frac {1}{2}},{\frac {3}{2}}+{\frac {n}{2}},{\frac {3}{2}}-{\frac {n}{2}};\,{\frac {{x}^{4}}{64}})} +{\frac {{\it \_C4}\, \left ( -\sqrt {2} \left ( {{\rm ber}_{-n}\left (x \right )} \right ) ^{2}n-\sqrt {2} \left ( {{\rm bei}_{-n}\left (x\right )} \right ) ^{2}n+{{\rm ber}_{-n}\left (x\right )}{{\rm ber}_{1-n}\left (x \right )}x-{{\rm ber}_{1-n}\left (x\right )}{{\rm bei}_{-n}\left (x \right )}x+{{\rm ber}_{-n}\left (x\right )}{{\rm bei}_{1-n}\left (x \right )}x+{{\rm bei}_{-n}\left (x\right )}{{\rm bei}_{1-n}\left (x \right )}x \right ) }{x}} \right \} \]