\[ -2 \left (x^2-a\right ) y'(x)+2 n x y(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0460383 (sec), leaf count = 65
DSolve[2*n*x*y[x] - 2*(-a + x^2)*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {Hypergeometric1F1}\left (-\frac {n}{2},a+\frac {1}{2},x^2\right )+i^{1-2 a} c_2 x^{1-2 a} \operatorname {Hypergeometric1F1}\left (-a-\frac {n}{2}+\frac {1}{2},\frac {3}{2}-a,x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.115 (sec), leaf count = 29
dsolve(x*diff(diff(y(x),x),x)-2*(x^2-a)*diff(y(x),x)+2*n*x*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \operatorname {KummerM}\left (-\frac {n}{2}, \frac {1}{2}+a , x^{2}\right )+c_{2} \operatorname {KummerU}\left (-\frac {n}{2}, \frac {1}{2}+a , x^{2}\right )\]