\[ a y(x)+x^6 y^{(3)}(x)+6 x^5 y''(x)=0 \] ✓ Mathematica : cpu = 0.43445 (sec), leaf count = 102
\[\left \{\left \{y(x)\to c_1 e^{\frac {\sqrt [3]{a}}{x}} \left (2 x-\sqrt [3]{a}\right )+c_2 e^{\frac {(-1)^{2/3} \sqrt [3]{a}}{x}} \left (x-\frac {1}{2} (-1)^{2/3} \sqrt [3]{a}\right )+c_3 e^{-\frac {\sqrt [3]{-1} \sqrt [3]{a}}{x}} \left (\frac {1}{2} \sqrt [3]{-1} \sqrt [3]{a}+x\right )\right \}\right \}\]
✓ Maple : cpu = 0.487 (sec), leaf count = 142
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( 2\,ax+\sqrt [3]{-{a}^{4}} \right ) {{\rm e}^{-{\frac {1}{ax}\sqrt [3]{-{a}^{4}}}}}+{\it \_C2}\, \left ( -4\,iax+i\sqrt [3]{-{a}^{4}}-\sqrt [3]{-{a}^{4}}\sqrt {3} \right ) {{\rm e}^{{\frac {-{\frac {i}{2}} \left ( -\sqrt {3}+i \right ) }{ax}\sqrt [3]{-{a}^{4}}}}}+{\it \_C3}\,{{\rm e}^{{\frac {-{\frac {i}{2}} \left ( \sqrt {3}+i \right ) }{ax}\sqrt [3]{-{a}^{4}}}}} \left ( \sqrt [3]{-{a}^{4}}\sqrt {3}-4\,iax+i\sqrt [3]{-{a}^{4}} \right ) \right \} \]