\[ \left (a x^3-12\right ) y(x)+6 x^2 y''(x)+x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.534067 (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 = 0.675 (sec), leaf count = 135
\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{3}} \left ( -{\it \_C2}\, \left ( \left ( -i-\sqrt {3} \right ) \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}}+i{a}^{3}x \right ) {{\rm e}^{{\frac {{\frac {i}{2}} \left ( i-\sqrt {3} \right ) x}{a}\sqrt [3]{-{a}^{4}}}}}- \left ( \left ( -i+\sqrt {3} \right ) \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}}+i{a}^{3}x \right ) {\it \_C3}\,{{\rm e}^{{\frac {{\frac {i}{2}} \left ( \sqrt {3}+i \right ) x}{a}\sqrt [3]{-{a}^{4}}}}}+{\it \_C1}\,{{\rm e}^{{\frac {x}{a}\sqrt [3]{-{a}^{4}}}}} \left ( {a}^{3}x+2\, \left ( -{a}^{4} \right ) ^{2/3} \right ) \right ) } \right \} \]