\[ y(x) \left (-a^2+x^2 (2 a+2 n+1)+a (-1)^n-x^4\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.333472 (sec), leaf count = 191
\[\left \{\left \{y(x)\to \frac {e^{-\frac {x^2}{2}} 2^{\frac {1}{4} \left (\sqrt {4 a^2-4 a (-1)^n+1}+2\right )} \left (x^2\right )^{\frac {1}{4} \left (\sqrt {4 a^2-4 a (-1)^n+1}+2\right )} \left (c_1 U\left (\frac {1}{4} \left (-2 a-2 n+\sqrt {4 a^2-4 (-1)^n a+1}+1\right ),\frac {1}{2} \left (\sqrt {4 a^2-4 (-1)^n a+1}+2\right ),x^2\right )+c_2 L_{\frac {1}{4} \left (2 a+2 n-\sqrt {4 a^2-4 (-1)^n a+1}-1\right )}^{\frac {1}{2} \sqrt {4 a^2-4 (-1)^n a+1}}\left (x^2\right )\right )}{\sqrt {x}}\right \}\right \}\]
✓ Maple : cpu = 0.606 (sec), leaf count = 71
\[ \left \{ y \left ( x \right ) ={1 \left ( {\it \_C2}\,{{\sl W}_{{\frac {n}{2}}+{\frac {a}{2}}+{\frac {1}{4}},\,{\frac {1}{4}\sqrt {1-4\, \left ( -1 \right ) ^{n}a+4\,{a}^{2}}}}\left ({x}^{2}\right )}+{\it \_C1}\,{{\sl M}_{{\frac {n}{2}}+{\frac {a}{2}}+{\frac {1}{4}},\,{\frac {1}{4}\sqrt {1-4\, \left ( -1 \right ) ^{n}a+4\,{a}^{2}}}}\left ({x}^{2}\right )} \right ) {\frac {1}{\sqrt {x}}}} \right \} \]