\[ \left (a x^3-12\right ) y(x)+x^3 y^{(3)}(x)+6 x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.737545 (sec), leaf count = 102
\[\left \{\left \{y(x)\to \frac {c_1 e^{-\sqrt [3]{a} x} \left (\sqrt [3]{a} x+2\right )}{x^3}+\frac {c_2 e^{\sqrt [3]{-1} \sqrt [3]{a} x} \left (\sqrt [3]{a} x+2 (-1)^{2/3}\right )}{x^3}+\frac {c_3 e^{-(-1)^{2/3} \sqrt [3]{a} x} \left (\sqrt [3]{a} x-2 \sqrt [3]{-1}\right )}{x^3}\right \}\right \}\]
✓ Maple : cpu = 0.503 (sec), leaf count = 151
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{{x}^{3}} \left ( {a}^{3}x+2\, \left ( -{a}^{4} \right ) ^{2/3} \right ) {{\rm e}^{{\frac {x}{a}\sqrt [3]{-{a}^{4}}}}}}+{\frac {{\it \_C2}}{{x}^{3}} \left ( -i{a}^{3}x+i \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}}- \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}}\sqrt {3} \right ) {{\rm e}^{{\frac {{\frac {i}{2}} \left ( \sqrt {3}+i \right ) x}{a}\sqrt [3]{-{a}^{4}}}}}}+{\frac {{\it \_C3}}{{x}^{3}}{{\rm e}^{{\frac {{\frac {i}{2}} \left ( -\sqrt {3}+i \right ) x}{a}\sqrt [3]{-{a}^{4}}}}} \left ( \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}}\sqrt {3}-i{a}^{3}x+i \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}} \right ) } \right \} \]