\[ 2 \left (2 a+4 x^2-1\right ) y'(x)-8 a x y(x)+y^{(3)}(x)-6 x y''(x)=0 \] ✓ Mathematica : cpu = 0.0865646 (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 = 0.148 (sec), leaf count = 59
\[ \left \{ y \left ( x \right ) ={x}^{2} \left ( \left ( {{\sl U}\left ({\frac {1}{2}}-{\frac {a}{4}},\,{\frac {3}{2}},\,{x}^{2}\right )} \right ) ^{2}{\it \_C2}+{{\sl U}\left ({\frac {1}{2}}-{\frac {a}{4}},\,{\frac {3}{2}},\,{x}^{2}\right )}{{\sl M}\left ({\frac {1}{2}}-{\frac {a}{4}},\,{\frac {3}{2}},\,{x}^{2}\right )}{\it \_C3}+ \left ( {{\sl M}\left ({\frac {1}{2}}-{\frac {a}{4}},\,{\frac {3}{2}},\,{x}^{2}\right )} \right ) ^{2}{\it \_C1} \right ) \right \} \]