\[ a x y'(x)+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.010781 (sec), leaf count = 78
DSolve[b*y[x] + a*x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-\frac {a x^2}{2}} \operatorname {HermiteH}\left (\frac {b-a}{a},\frac {\sqrt {a} x}{\sqrt {2}}\right )+c_2 e^{-\frac {a x^2}{2}} \operatorname {Hypergeometric1F1}\left (-\frac {b-a}{2 a},\frac {1}{2},\frac {a x^2}{2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.109 (sec), leaf count = 58
dsolve(diff(diff(y(x),x),x)+a*x*diff(y(x),x)+b*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {a \,x^{2}}{2}} x \left (\operatorname {KummerU}\left (\frac {2 a -b}{2 a}, \frac {3}{2}, \frac {a \,x^{2}}{2}\right ) c_{2}+\operatorname {KummerM}\left (\frac {2 a -b}{2 a}, \frac {3}{2}, \frac {a \,x^{2}}{2}\right ) c_{1}\right )\]