\[ y(x) \left (a x^4+(n-2) n (n+1) (n+3)\right )-2 n (n+1) x^2 y''(x)+4 n (n+1) x y'(x)+x^4 y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 4.62015 (sec), leaf count = 310
\[\left \{\left \{y(x)\to \sqrt [8]{a} 2^{-n-\frac {7}{2}} \sqrt {x} \left (2^{2 n+1} \text {ber}_{-n-\frac {1}{2}}\left (\sqrt [4]{a} x\right ) \left (4 c_2 \cos \left (\frac {3}{8} \pi (2 n+1)\right ) \Gamma \left (\frac {1}{2}-n\right )-c_1 \cos \left (\frac {3}{8} \pi (2 n-3)\right ) \Gamma \left (\frac {3}{2}-n\right )\right )+\text {ber}_{n+\frac {1}{2}}\left (\sqrt [4]{a} x\right ) \left (4 c_3 \cos \left (\frac {3}{8} \pi (2 n+1)\right ) \Gamma \left (n+\frac {3}{2}\right )-c_4 \cos \left (\frac {3}{8} \pi (2 n+5)\right ) \Gamma \left (n+\frac {5}{2}\right )\right )+c_1 2^{2 n+1} \sin \left (\frac {3}{8} \pi (2 n-3)\right ) \Gamma \left (\frac {3}{2}-n\right ) \text {bei}_{-n-\frac {1}{2}}\left (\sqrt [4]{a} x\right )-c_2 2^{2 n+3} \sin \left (\frac {3}{8} \pi (2 n+1)\right ) \Gamma \left (\frac {1}{2}-n\right ) \text {bei}_{-n-\frac {1}{2}}\left (\sqrt [4]{a} x\right )+4 c_3 \sin \left (\frac {3}{8} \pi (2 n+1)\right ) \Gamma \left (n+\frac {3}{2}\right ) \text {bei}_{n+\frac {1}{2}}\left (\sqrt [4]{a} x\right )-c_4 \sin \left (\frac {3}{8} \pi (2 n+5)\right ) \Gamma \left (n+\frac {5}{2}\right ) \text {bei}_{n+\frac {1}{2}}\left (\sqrt [4]{a} x\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.288 (sec), leaf count = 69
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {{\sl Y}_{n+{\frac {1}{2}}}\left (\sqrt {-\sqrt {-a}}x\right )}{\it \_C4}+{{\sl J}_{n+{\frac {1}{2}}}\left (\sqrt {-\sqrt {-a}}x\right )}{\it \_C3}+{{\sl Y}_{n+{\frac {1}{2}}}\left (\sqrt [4]{-a}x\right )}{\it \_C2}+{{\sl J}_{n+{\frac {1}{2}}}\left (\sqrt [4]{-a}x\right )}{\it \_C1} \right ) \right \} \]