\[ a^2 x^2 y(x)+2 a x y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0233135 (sec), leaf count = 57
DSolve[a^2*x^2*y[x] + 2*a*x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{-\frac {a x^2}{2}-\sqrt {a} x}+\frac {c_2 e^{\sqrt {a} x-\frac {a x^2}{2}}}{2 \sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.048 (sec), leaf count = 35
dsolve(diff(diff(y(x),x),x)+2*a*x*diff(y(x),x)+a^2*x^2*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x \left (a x -2 \sqrt {a}\right )}{2}}+c_{2} {\mathrm e}^{-\frac {x \left (a x +2 \sqrt {a}\right )}{2}}\]