\[ a x^2 y(x)+x^2 y^{(3)}(x)+6 y'(x)+6 x y''(x)=0 \] ✓ Mathematica : cpu = 0.193293 (sec), leaf count = 63
\[\left \{\left \{y(x)\to \frac {c_1 e^{-\sqrt [3]{a} x}}{x^2}+\frac {c_2 e^{\sqrt [3]{-1} \sqrt [3]{a} x}}{x^2}+\frac {c_3 e^{-(-1)^{2/3} \sqrt [3]{a} x}}{x^2}\right \}\right \}\] ✓ Maple : cpu = 0.046 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{2}} \left ( {\it \_C1}\,{{\rm e}^{{\frac { \left ( -1+i\sqrt {3} \right ) x}{2}\sqrt [3]{-a}}}}+{\it \_C2}\,{{\rm e}^{-{\frac { \left ( 1+i\sqrt {3} \right ) x}{2}\sqrt [3]{-a}}}}+{\it \_C3}\,{{\rm e}^{\sqrt [3]{-a}x}} \right ) } \right \} \]