\[ \left (4 n^2-4 x^4-1\right ) y(x)-\left (4 n^2-1\right ) x^2 y''(x)-\left (4 n^2-1\right ) x y'(x)+x^4 y^{(4)}(x)+4 x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 2.34916 (sec), leaf count = 187
\[\left \{\left \{y(x)\to \frac {\sqrt [4]{-1} \left (x^2 \left (c_2 \, _0F_3\left (;\frac {3}{2},1-\frac {n}{2},\frac {n}{2}+1;\frac {x^4}{64}\right )+c_3 \left (\frac {i}{8}\right )^{-n} x^{-2 n} \, _0F_3\left (;1-n,1-\frac {n}{2},\frac {3}{2}-\frac {n}{2};\frac {x^4}{64}\right )+c_4 \left (\frac {i}{8}\right )^n x^{2 n} \, _0F_3\left (;\frac {n}{2}+1,\frac {n}{2}+\frac {3}{2},n+1;\frac {x^4}{64}\right )\right )-8 i c_1 \, _0F_3\left (;\frac {1}{2},\frac {1}{2}-\frac {n}{2},\frac {n}{2}+\frac {1}{2};\frac {x^4}{64}\right )\right )}{2 \sqrt {2} x}\right \}\right \}\]
✓ Maple : cpu = 0.398 (sec), leaf count = 87
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {\it \_C4}\,{\mbox {$_0$F$_3$}(\ ;\,{\frac {1}{2}},-{\frac {n}{2}}+{\frac {1}{2}},{\frac {n}{2}}+{\frac {1}{2}};\,{\frac {{x}^{4}}{64}})}+ \left ( {\it \_C3}\,{\mbox {$_0$F$_3$}(\ ;\,{\frac {3}{2}},-{\frac {n}{2}}+1,{\frac {n}{2}}+1;\,{\frac {{x}^{4}}{64}})}+{\it \_C2}\, \left ( {{\rm bei}_{-n}\left (x\right )} \right ) ^{2}+ \left ( {{\rm ber}_{-n}\left (x\right )} \right ) ^{2}{\it \_C2}+{\it \_C1}\, \left ( \left ( {{\rm ber}_{n}\left (x\right )} \right ) ^{2}+ \left ( {{\rm bei}_{n}\left (x\right )} \right ) ^{2} \right ) \right ) {x}^{2} \right ) } \right \} \]