\[ \boxed { {x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +3\,x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 4\,{a}^{2}{x}^{2\,a}+1-4\,{\nu }^{2}{a}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =4\,{a}^{3}{x}^{2\,a-1}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.046006 (sec), leaf count = 102 \[ \left \{\left \{y(x)\to c_2 \left (x^{2 a}\right )^{-\nu } \, _1F_2\left (-\nu -\frac {1}{2};1-2 \nu ,1-\nu ;-x^{2 a}\right )+c_3 \left (x^{2 a}\right )^{\nu } \, _1F_2\left (\nu -\frac {1}{2};\nu +1,2 \nu +1;-x^{2 a}\right )+c_1 \, _1F_2\left (-\frac {1}{2};1-\nu ,\nu +1;-x^{2 a}\right )\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 88 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_1$F$_2$}(-{\frac {1}{2}};\,\nu +1,-\nu +1;\,-{x}^{2\,a})}+{\it \_C2}\,{x}^{-2\,a\nu } {\mbox {$_1$F$_2$}(-{\frac {1}{2}}-\nu ;\,1-2\,\nu ,-\nu +1;\,-{x}^{2\,a})} +{\it \_C3}\,{x}^{2\,a\nu } {\mbox {$_1$F$_2$}(\nu -{\frac {1}{2}};\,2\,\nu +1,\nu +1;\,-{x}^{2\,a})} \right \} \]