\[ \boxed { {x}^{4}{\it d4y} \left ( x \right ) +4\,{x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( 4\,{n}^{2}-1 \right ) {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 4\,{n}^{2}-1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -4\,y \left ( x \right ) {x}^{4}=0} \]
Mathematica: cpu = 1.107641 (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 = 0.187 (sec), leaf count = 93 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{n}\left ( \left ( { \frac {1}{2}}-{\frac {i}{2}} \right ) \sqrt {2}x\right )}{{\sl J}_{n }\left ( \left ( {\frac {1}{2}}+{\frac {i}{2}} \right ) \sqrt {2}x \right )}+{\it \_C2}\,{{\sl J}_{n}\left ( \left ( {\frac {1}{2}}-{\frac { i}{2}} \right ) \sqrt {2}x\right )}{{\sl Y}_{n}\left ( \left ( {\frac {1}{ 2}}+{\frac {i}{2}} \right ) \sqrt {2}x\right )}+{\it \_C3}\,{{\sl Y}_{n }\left ( \left ( {\frac {1}{2}}-{\frac {i}{2}} \right ) \sqrt {2}x \right )}{{\sl J}_{n}\left ( \left ( {\frac {1}{2}}+{\frac {i}{2}} \right ) \sqrt {2}x\right )}+{\it \_C4}\,{{\sl Y}_{n}\left ( \left ( { \frac {1}{2}}-{\frac {i}{2}} \right ) \sqrt {2}x\right )}{{\sl Y}_{n }\left ( \left ( {\frac {1}{2}}+{\frac {i}{2}} \right ) \sqrt {2}x \right )} \right \} \]