\[ \boxed { {x}^{3}{\it d4y} \left ( x \right ) +2\,{x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{a}^{4}{x}^{3}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.264534 (sec), leaf count = 100 \[ \left \{\left \{y(x)\to c_4 G_{0,4}^{2,0}\left (\frac {a^4 x^4}{256}| \begin {array}{c} 0,0,\frac {1}{2},\frac {1}{2} \\ \end {array} \right )+c_2 G_{0,4}^{2,0}\left (\frac {a^4 x^4}{256}| \begin {array}{c} \frac {1}{2},\frac {1}{2},0,0 \\ \end {array} \right )+\frac {1}{8} i c_1 (I_0(a x)-J_0(a x))+\frac {1}{2} c_3 (J_0(a x)+I_0(a x))\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl I}_{0}\left (ax\right )}+ {\it \_C2}\,{{\sl J}_{0}\left (ax\right )}+{\it \_C3}\,{{\sl K}_{0 }\left (ax\right )}+{\it \_C4}\,{{\sl Y}_{0}\left (ax\right )} \right \} \]