\[ \left (4 n^2-4 x^4-1\right ) y(x)-\left (4 n^2-1\right ) x^2 y''(x)-\left (4 n^2-1\right ) x y'(x)+x^4 y^{(4)}(x)+4 x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 1.48094 (sec), leaf count = 232
\[\left \{\left \{y(x)\to \frac {\sqrt [4]{-1} c_2 x \, _0F_3\left (;\frac {3}{2},1-\frac {n}{2},\frac {n}{2}+1;\frac {x^4}{64}\right )}{2 \sqrt {2}}-\frac {2 (-1)^{3/4} \sqrt {2} c_1 \, _0F_3\left (;\frac {1}{2},\frac {1}{2}-\frac {n}{2},\frac {n}{2}+\frac {1}{2};\frac {x^4}{64}\right )}{x}+c_3 (-1)^{\frac {1}{4} (1-2 n)} 2^{2 n+\frac {1}{2} (2 n-1)-1} x^{1-2 n} \, _0F_3\left (;1-n,1-\frac {n}{2},\frac {3}{2}-\frac {n}{2};\frac {x^4}{64}\right )+c_4 (-1)^{\frac {1}{4} (2 n+1)} 2^{\frac {1}{2} (-2 n-1)-2 n-1} x^{2 n+1} \, _0F_3\left (;\frac {n}{2}+1,\frac {n}{2}+\frac {3}{2},n+1;\frac {x^4}{64}\right )\right \}\right \}\] ✓ Maple : cpu = 0.217 (sec), leaf count = 87
\[y \relax (x ) = \frac {c_{4} \hypergeom \left (\left [\right ], \left [\frac {1}{2}, \frac {n}{2}+\frac {1}{2}, -\frac {n}{2}+\frac {1}{2}\right ], \frac {x^{4}}{64}\right )+x^{2} \left (\hypergeom \left (\left [\right ], \left [\frac {3}{2}, -\frac {n}{2}+1, \frac {n}{2}+1\right ], \frac {x^{4}}{64}\right ) c_{3}+c_{2} \mathit {bei}_{-n}\relax (x )^{2}+\mathit {ber}_{-n}\relax (x )^{2} c_{2}+c_{1} \left (\mathit {ber}_{n}\relax (x )^{2}+\mathit {bei}_{n}\relax (x )^{2}\right )\right )}{x}\]