\[ a y(x)+y''(x)-2 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0049645 (sec), leaf count = 31
DSolve[a*y[x] - 2*x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {HermiteH}\left (\frac {a}{2},x\right )+c_2 \operatorname {Hypergeometric1F1}\left (-\frac {a}{4},\frac {1}{2},x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.1 (sec), leaf count = 31
dsolve(diff(diff(y(x),x),x)-2*x*diff(y(x),x)+a*y(x)=0,y(x))
\[y \left (x \right ) = x \left (\operatorname {KummerM}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) c_{1}+\operatorname {KummerU}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) c_{2}\right )\]