\[ y(x) \left (a \left ((-1)^n-1\right )+2 n x^2\right )-2 x \left (x^2-a\right ) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.193953 (sec), leaf count = 252
DSolve[((-1 + (-1)^n)*a + 2*n*x^2)*y[x] - 2*x*(-a + x^2)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 (-1)^{\frac {1}{4} \left (-\sqrt {4 a^2-4 a (-1)^n+1}-2 a+1\right )} x^{\frac {1}{2} \left (-\sqrt {4 a^2-4 a (-1)^n+1}-2 a+1\right )} \, _1F_1\left (-\frac {a}{2}-\frac {n}{2}-\frac {1}{4} \sqrt {4 a^2-4 (-1)^n a+1}+\frac {1}{4};1-\frac {1}{2} \sqrt {4 a^2-4 (-1)^n a+1};x^2\right )+c_2 (-1)^{\frac {1}{4} \left (\sqrt {4 a^2-4 a (-1)^n+1}-2 a+1\right )} x^{\frac {1}{2} \left (\sqrt {4 a^2-4 a (-1)^n+1}-2 a+1\right )} \, _1F_1\left (-\frac {a}{2}-\frac {n}{2}+\frac {1}{4} \sqrt {4 a^2-4 (-1)^n a+1}+\frac {1}{4};\frac {1}{2} \sqrt {4 a^2-4 (-1)^n a+1}+1;x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.181 (sec), leaf count = 81
dsolve(x^2*diff(diff(y(x),x),x)-2*x*(x^2-a)*diff(y(x),x)+(2*n*x^2+((-1)^n-1)*a)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{\frac {x^{2}}{2}} x^{-\frac {1}{2}-a} \left (\WhittakerW \left (\frac {n}{2}+\frac {a}{2}+\frac {1}{4}, \frac {\sqrt {1-4 \left (-1\right )^{n} a +4 a^{2}}}{4}, x^{2}\right ) c_{2}+\WhittakerM \left (\frac {n}{2}+\frac {a}{2}+\frac {1}{4}, \frac {\sqrt {1-4 \left (-1\right )^{n} a +4 a^{2}}}{4}, x^{2}\right ) c_{1}\right )\]