\[ \left (a x^3-12\right ) y(x)+x^3 y^{(3)}(x)+6 x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.68781 (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 = 0.478 (sec), leaf count = 135
\[\left \{y \left (x \right ) = \frac {c_{1} \left (a^{3} x +2 \left (-a^{4}\right )^{\frac {2}{3}}\right ) {\mathrm e}^{\frac {\left (-a^{4}\right )^{\frac {1}{3}} x}{a}}-c_{2} \left (i a^{3} x +\left (-i+\sqrt {3}\right ) \left (-a^{4}\right )^{\frac {2}{3}}\right ) {\mathrm e}^{\frac {i \left (\sqrt {3}+i\right ) \left (-a^{4}\right )^{\frac {1}{3}} x}{2 a}}-c_{3} \left (i a^{3} x +\left (-i-\sqrt {3}\right ) \left (-a^{4}\right )^{\frac {2}{3}}\right ) {\mathrm e}^{\frac {i \left (i-\sqrt {3}\right ) \left (-a^{4}\right )^{\frac {1}{3}} x}{2 a}}}{x^{3}}\right \}\]