\[ -\left (12 n^2+4 x^4-3\right ) y(x)-\left (4 n^2+3\right ) x^2 y''(x)+\left (12 n^2-3\right ) x y'(x)+x^4 y^{(4)}(x)+4 x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 1.31805 (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 = 0.273 (sec), leaf count = 164
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( \left ( {{\rm ber}_{n}\left (x\right )} \right ) ^{2}+ \left ( {{\rm bei}_{n}\left (x\right )} \right ) ^{2} \right ) }{x}}+{\it \_C2}\,{x}^{3}{\mbox {$_0$F$_3$}(\ ;\,{\frac {3}{2}},2-{\frac {n}{2}},2+{\frac {n}{2}};\,{\frac {{x}^{4}}{64}})}+{\it \_C3}\,x{\mbox {$_0$F$_3$}(\ ;\,{\frac {1}{2}},{\frac {3}{2}}-{\frac {n}{2}},{\frac {3}{2}}+{\frac {n}{2}};\,{\frac {{x}^{4}}{64}})}+{\frac {{\it \_C4}\, \left ( -\sqrt {2}{{\rm ber}_{-n}\left (x\right )}{{\rm ber}_{1-n}\left (x\right )}x-\sqrt {2}{{\rm ber}_{-n}\left (x\right )}{{\rm bei}_{1-n}\left (x\right )}x+\sqrt {2}{{\rm ber}_{1-n}\left (x\right )}{{\rm bei}_{-n}\left (x\right )}x-\sqrt {2}{{\rm bei}_{-n}\left (x\right )}{{\rm bei}_{1-n}\left (x\right )}x+2\, \left ( {{\rm ber}_{-n}\left (x\right )} \right ) ^{2}n+2\, \left ( {{\rm bei}_{-n}\left (x\right )} \right ) ^{2}n \right ) }{x}} \right \} \]