\[ a y(x)+x^6 y^{(3)}(x)+6 x^5 y''(x)=0 \] ✓ Mathematica : cpu = 0.486336 (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 = 0.604 (sec), leaf count = 291
\[ \left \{ y \left ( x \right ) ={{\it \_C1}\, \left ( -8\,{x}^{3}+a \right ) ^{4}{{\rm e}^{-{\frac {1}{ax}\sqrt [3]{-{a}^{4}}}}} \left ( 2\,ax+\sqrt [3]{-{a}^{4}} \right ) ^{-3} \left ( 4\,{a}^{2}{x}^{2}-2\,x\sqrt [3]{-{a}^{4}}a+ \left ( -{a}^{4} \right ) ^{{\frac {2}{3}}} \right ) ^{-4}}+{{\it \_C2}\, \left ( -8\,{x}^{3}+a \right ) ^{4}{{\rm e}^{{\frac {-{\frac {i}{2}} \left ( -\sqrt {3}+i \right ) }{ax}\sqrt [3]{-{a}^{4}}}}} \left ( -4\,iax+i\sqrt [3]{-{a}^{4}}-\sqrt [3]{-{a}^{4}}\sqrt {3} \right ) ^{-3} \left ( \sqrt [3]{-{a}^{4}}\sqrt {3}-4\,iax+i\sqrt [3]{-{a}^{4}} \right ) ^{-4} \left ( 2\,ax+\sqrt [3]{-{a}^{4}} \right ) ^{-4}}+{{\it \_C3}\, \left ( -8\,{x}^{3}+a \right ) ^{4}{{\rm e}^{{\frac {-{\frac {i}{2}} \left ( \sqrt {3}+i \right ) }{ax}\sqrt [3]{-{a}^{4}}}}} \left ( \sqrt [3]{-{a}^{4}}\sqrt {3}-4\,iax+i\sqrt [3]{-{a}^{4}} \right ) ^{-3} \left ( -4\,iax+i\sqrt [3]{-{a}^{4}}-\sqrt [3]{-{a}^{4}}\sqrt {3} \right ) ^{-4} \left ( 2\,ax+\sqrt [3]{-{a}^{4}} \right ) ^{-4}} \right \} \]