\[ y(x) \left (a \left ((-1)^n-1\right )+2 n x^2\right )-2 x \left (x^2-a\right ) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.205646 (sec), leaf count = 252
\[\left \{\left \{y(x)\to c_1 (-1)^{\frac {1}{4} \left (-\sqrt {4 a^2-4 a (-1)^n+1}-2 a+1\right )} x^{\frac {1}{2} \left (-\sqrt {4 a^2-4 a (-1)^n+1}-2 a+1\right )} \, _1F_1\left (-\frac {a}{2}-\frac {n}{2}-\frac {1}{4} \sqrt {4 a^2-4 (-1)^n a+1}+\frac {1}{4};1-\frac {1}{2} \sqrt {4 a^2-4 (-1)^n a+1};x^2\right )+c_2 (-1)^{\frac {1}{4} \left (\sqrt {4 a^2-4 a (-1)^n+1}-2 a+1\right )} x^{\frac {1}{2} \left (\sqrt {4 a^2-4 a (-1)^n+1}-2 a+1\right )} \, _1F_1\left (-\frac {a}{2}-\frac {n}{2}+\frac {1}{4} \sqrt {4 a^2-4 (-1)^n a+1}+\frac {1}{4};\frac {1}{2} \sqrt {4 a^2-4 (-1)^n a+1}+1;x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.462 (sec), leaf count = 81
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {{x}^{2}}{2}}}}{x}^{-{\frac {1}{2}}-a} \left ( {{\sl M}_{{\frac {n}{2}}+{\frac {a}{2}}+{\frac {1}{4}},\,{\frac {1}{4}\sqrt {1-4\, \left ( -1 \right ) ^{n}a+4\,{a}^{2}}}}\left ({x}^{2}\right )}{\it \_C1}+{{\sl W}_{{\frac {n}{2}}+{\frac {a}{2}}+{\frac {1}{4}},\,{\frac {1}{4}\sqrt {1-4\, \left ( -1 \right ) ^{n}a+4\,{a}^{2}}}}\left ({x}^{2}\right )}{\it \_C2} \right ) \right \} \]