\[ a x^2 y(x)+x^2 y^{(3)}(x)+6 x y''(x)+6 y'(x)=0 \] ✓ Mathematica : cpu = 0.138353 (sec), leaf count = 63
DSolve[a*x^2*y[x] + 6*Derivative[1][y][x] + 6*x*Derivative[2][y][x] + x^2*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 e^{-\sqrt [3]{a} x}}{x^2}+\frac {c_2 e^{\sqrt [3]{-1} \sqrt [3]{a} x}}{x^2}+\frac {c_3 e^{-(-1)^{2/3} \sqrt [3]{a} x}}{x^2}\right \}\right \}\] ✓ Maple : cpu = 0.017 (sec), leaf count = 57
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+6*x*diff(diff(y(x),x),x)+6*diff(y(x),x)+y(x)*a*x^2=0,y(x))
\[y \left (x \right ) = \frac {c_{1} {\mathrm e}^{\frac {\left (-a \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {\left (-a \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right ) x}{2}}+c_{3} {\mathrm e}^{\left (-a \right )^{\frac {1}{3}} x}}{x^{2}}\]