\[ \left (a x^3-12\right ) y(x)+x^3 y^{(3)}(x)+6 x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.525427 (sec), leaf count = 102
DSolve[(-12 + a*x^3)*y[x] + 6*x^2*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 e^{-\sqrt [3]{a} x} \left (\sqrt [3]{a} x+2\right )}{x^3}+\frac {c_2 e^{\sqrt [3]{-1} \sqrt [3]{a} x} \left (\sqrt [3]{a} x+2 (-1)^{2/3}\right )}{x^3}+\frac {c_3 e^{-(-1)^{2/3} \sqrt [3]{a} x} \left (\sqrt [3]{a} x-2 \sqrt [3]{-1}\right )}{x^3}\right \}\right \}\] ✓ Maple : cpu = 0.424 (sec), leaf count = 135
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+6*x^2*diff(diff(y(x),x),x)+(a*x^3-12)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {-c_{2} \left (\left (-i-\sqrt {3}\right ) \left (-a^{4}\right )^{\frac {2}{3}}+i a^{3} x \right ) {\mathrm e}^{\frac {i \left (i-\sqrt {3}\right ) \left (-a^{4}\right )^{\frac {1}{3}} x}{2 a}}-\left (\left (-i+\sqrt {3}\right ) \left (-a^{4}\right )^{\frac {2}{3}}+i a^{3} x \right ) c_{3} {\mathrm e}^{\frac {i \left (\sqrt {3}+i\right ) \left (-a^{4}\right )^{\frac {1}{3}} x}{2 a}}+c_{1} {\mathrm e}^{\frac {\left (-a^{4}\right )^{\frac {1}{3}} x}{a}} \left (a^{3} x +2 \left (-a^{4}\right )^{\frac {2}{3}}\right )}{x^{3}}\]