\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -6\,x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\, \left ( 4\,{x}^{2}+2\,a-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -8\,axy \left ( x \right ) =0} \]
Mathematica: cpu = 0.087011 (sec), leaf count = 57 \[ \left \{\left \{y(x)\to c_2 H_{\frac {a}{2}}(x) \, _1F_1\left (-\frac {a}{4};\frac {1}{2};x^2\right )+c_1 H_{\frac {a}{2}}(x){}^2+c_3 \, _1F_1\left (-\frac {a}{4};\frac {1}{2};x^2\right ){}^2\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 64 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {{\sl M}\left ({\frac {1}{2}}-{\frac {a}{4}},\,{\frac {3}{2}},\,{x}^{2}\right )} \right ) ^{2} {x}^{2}+{\it \_C2}\, \left ( {{\sl U}\left ({\frac {1}{2}}-{\frac {a}{4} },\,{\frac {3}{2}},\,{x}^{2}\right )} \right ) ^{2}{x}^{2}+{\it \_C3}\,{ {\sl M}\left ({\frac {1}{2}}-{\frac {a}{4}},\,{\frac {3}{2}},\,{x}^{2} \right )}{x}^{2}{{\sl U}\left ({\frac {1}{2}}-{\frac {a}{4}},\,{\frac {3 }{2}},\,{x}^{2}\right )} \right \} \]