\[ -\left (4 n^2-1\right ) x^2 y''(x)+\left (4 n^2-1\right ) x y'(x)+x^4 y^{(4)}(x)-4 x^4 y(x)+4 x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 1.246 (sec), leaf count = 140
\[\left \{\left \{y(x)\to c_1 \, _0F_3\left (;\frac {1}{2},1-\frac {n}{2},\frac {n}{2}+1;\frac {x^4}{64}\right )+\frac {1}{8} i c_2 x^2 \, _0F_3\left (;\frac {3}{2},\frac {3}{2}-\frac {n}{2},\frac {n}{2}+\frac {3}{2};\frac {x^4}{64}\right )+c_3 \left (\frac {i}{2}\right )^{-n} \Gamma (1-n)^2 \left (\text {ber}_{-n}(x){}^2+\text {bei}_{-n}(x){}^2\right )+c_4 \left (\frac {i}{2}\right )^n \Gamma (n+1)^2 \left (\text {ber}_n(x){}^2+\text {bei}_n(x){}^2\right )\right \}\right \}\]
✓ Maple : cpu = 0.448 (sec), leaf count = 77
\[ \left \{ y \left ( x \right ) = \left ( {{\sl Y}_{n}\left ( \left ( {\frac {1}{2}}-{\frac {i}{2}} \right ) \sqrt {2}x\right )}{\it \_C3}+{\it \_C1}\,{{\sl J}_{n}\left ( \left ( {\frac {1}{2}}-{\frac {i}{2}} \right ) \sqrt {2}x\right )} \right ) {{\sl J}_{n}\left ( \left ( {\frac {1}{2}}+{\frac {i}{2}} \right ) \sqrt {2}x\right )}+{{\sl Y}_{n}\left ( \left ( {\frac {1}{2}}+{\frac {i}{2}} \right ) \sqrt {2}x\right )} \left ( {{\sl Y}_{n}\left ( \left ( {\frac {1}{2}}-{\frac {i}{2}} \right ) \sqrt {2}x\right )}{\it \_C4}+{\it \_C2}\,{{\sl J}_{n}\left ( \left ( {\frac {1}{2}}-{\frac {i}{2}} \right ) \sqrt {2}x\right )} \right ) \right \} \]