\[ y'(x) (a x+b+n)+a n y(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0396758 (sec), leaf count = 43
DSolve[a*n*y[x] + (b + n + a*x)*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-a x} U(b,b+n,a x)+c_2 e^{-a x} L_{-b}^{b+n-1}(a x)\right \}\right \}\] ✓ Maple : cpu = 0.082 (sec), leaf count = 31
dsolve(x*diff(diff(y(x),x),x)+(a*x+b+n)*diff(y(x),x)+n*a*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-a x} \left (\KummerM \left (b , b +n , a x \right ) c_{1}+\KummerU \left (b , b +n , a x \right ) c_{2}\right )\]