\[ \boxed { {x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +6\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( a{x}^{3}-12 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.717091 (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 = 0.390 (sec), leaf count = 151 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{{x}^{3}} \left ( {a}^{ 3}x+2\, \left ( -{a}^{4} \right ) ^{2/3} \right ) {{\rm e}^{{\frac {x}{a} \sqrt [3]{-{a}^{4}}}}}}+{\frac {{\it \_C2}}{{x}^{3}} \left ( \left ( -{ a}^{4} \right ) ^{{\frac {2}{3}}}\sqrt {3}-i{a}^{3}x+i \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}} \right ) {{\rm e}^{{\frac {{\frac {i}{2}} \left ( -\sqrt {3}+i \right ) x}{a}\sqrt [3]{-{a}^{4}}}}}}+{\frac {{ \it \_C3}}{{x}^{3}} \left ( -i{a}^{3}x+i \left ( -{a}^{4} \right ) ^{{ \frac {2}{3}}}- \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}}\sqrt {3} \right ) {{\rm e}^{{\frac {{\frac {i}{2}} \left ( \sqrt {3}+i \right ) x }{a}\sqrt [3]{-{a}^{4}}}}}} \right \} \]